Question Number 196544 by mr W last updated on 27/Aug/23
Answered by witcher3 last updated on 27/Aug/23
$$\mathrm{f}\left(\mathrm{k}+\mathrm{1}\right)=\mathrm{f}\left(\mathrm{1}\right)+\mathrm{f}\left(\mathrm{k}\right)+\mathrm{k} \\ $$$$\Rightarrow\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\left(\mathrm{f}\left(\mathrm{k}+\mathrm{1}\right)−\mathrm{f}\left(\mathrm{k}\right)\right)=\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\mathrm{f}\left(\mathrm{1}\right)+\mathrm{k}=\left(\mathrm{n}−\mathrm{1}\right)\mathrm{f}\left(\mathrm{1}\right)+\frac{\mathrm{n}}{\mathrm{2}}\left(\mathrm{n}−\mathrm{1}\right) \\ $$$$\mathrm{f}\left(\mathrm{n}\right)−\mathrm{f}\left(\mathrm{1}\right)=\frac{\left(\mathrm{n}−\mathrm{1}\right)\left(\mathrm{n}+\mathrm{2f}\left(\mathrm{1}\right)\right)}{\mathrm{2}} \\ $$$$\mathrm{f}\left(\mathrm{4}\right)=\mathrm{2f}\left(\mathrm{2}\right)+\mathrm{4}=\mathrm{10}\Rightarrow\mathrm{f}\left(\mathrm{2}\right)=\mathrm{3} \\ $$$$\mathrm{f}\left(\mathrm{2}\right)=\mathrm{2f}\left(\mathrm{1}\right)+\mathrm{1}=\mathrm{3}\Rightarrow\mathrm{f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$$\mathrm{f}\left(\mathrm{n}\right)−\mathrm{1}=\frac{\left(\mathrm{n}+\mathrm{2}\right)\left(\mathrm{n}−\mathrm{1}\right)}{\mathrm{2}} \\ $$$$\mathrm{f}\left(\mathrm{n}\right)=\frac{\mathrm{n}^{\mathrm{2}} +\mathrm{n}}{\mathrm{2}} \\ $$$$\mathrm{f}\left(\mathrm{2023}\right)=\mathrm{1012}.\mathrm{2023} \\ $$$$ \\ $$$$ \\ $$
Commented by mr W last updated on 27/Aug/23
$${great}\:{solution}!\:{thanks}\:{alot}! \\ $$
Commented by York12 last updated on 27/Aug/23
$${sir}\:{what}\:{calculus}\:{Book}\:{do}\:{you}\:{suggest} \\ $$
Commented by York12 last updated on 27/Aug/23
$${I}\:{am}\:{asking}\:{Witcher} \\ $$
Commented by witcher3 last updated on 27/Aug/23
$$\mathrm{you}\:\mathrm{are}\:\mathrm{welcom}\:\mathrm{sir} \\ $$
Commented by witcher3 last updated on 27/Aug/23
$$\mathrm{sir}\:\mathrm{York}\:\mathrm{for}\:\mathrm{calculus}\:\mathrm{and}\:\mathrm{Algebra}\:\mathrm{i}\:\mathrm{have}\:\mathrm{used}\:\mathrm{book}\:\mathrm{only}\:\mathrm{in}\:\mathrm{high}\:\mathrm{school}\: \\ $$$$\mathrm{books}\:\mathrm{in}\:\mathrm{Arabic}\:\mathrm{language}\: \\ $$$$\mathrm{for}\:\mathrm{the}\:\mathrm{rest}\:\mathrm{just}\:\mathrm{Google} \\ $$$$\mathrm{when}\:\mathrm{i}\:\mathrm{want}\:\:\mathrm{somthing}\:\mathrm{i}\:\mathrm{use}\:\mathrm{pdf}\:\mathrm{in}\:\mathrm{web}\: \\ $$$$\mathrm{withe}\:\mathrm{execice}\: \\ $$$$\mathrm{i}\:\mathrm{used}\:``\mathrm{The}\:\mathrm{Hatcher}''\:\mathrm{for}\:\mathrm{Topologie} \\ $$$$\mathrm{and}\:``\:\mathrm{Riemann}\:\mathrm{sirfaces}\:\mathrm{in}\:\mathrm{complex}\:\mathrm{plan}'' \\ $$$$\mathrm{all}\:\mathrm{The}\:\mathrm{reste}\:\mathrm{is}\:\mathrm{web}\: \\ $$
Commented by York12 last updated on 27/Aug/23
$${I}\:{am}\:{arabian} \\ $$
Commented by York12 last updated on 27/Aug/23
$${Where}\:{are}\:{you}\:{from}\:{sir} \\ $$$$ \\ $$
Commented by York12 last updated on 27/Aug/23
$${What}\:{arabic}\:{books}\:{have}\:{you}\:{used}\:{sir} \\ $$
Commented by York12 last updated on 27/Aug/23
$$ \\ $$من اي دولة انت يا استاذ انا حقا احتاج الى المساعدة
Commented by witcher3 last updated on 27/Aug/23
$$\mathrm{selAm}\:\mathrm{alaykoum}\: \\ $$$$\mathrm{1}−``\:\mathrm{El}\:\mathrm{moumtaz}\:'' \\ $$$$\mathrm{i}\:\mathrm{will}\:\mathrm{downoald}\:\mathrm{arabic}\:\mathrm{Keyboard} \\ $$$$ \\ $$
Commented by York12 last updated on 27/Aug/23
$$ \\ $$عليكم السلام ورحمة الله وبركاته
Commented by York12 last updated on 27/Aug/23
$$ \\ $$ممكن اسم المؤلف لاني ما وجدت الكتاب و هل يمكنك التواصل معي عبر الواتساب هاتفي هو +201551265014
Commented by York12 last updated on 27/Aug/23
$$ \\ $$ساكون شديد الامتنان و الشكر لك ان تواصلت معي ، ساكون في انتظارك
Commented by York12 last updated on 27/Aug/23
$$ \\ $$و ان وجدت مشكلة في الواتساب فانا ليس لدي مانع في اي منصة تزاصل اجتماعي اخرى للتواصل فقط اعلمني
Commented by York12 last updated on 28/Aug/23
$$ \\ $$حضرتك لم تجبني
Commented by witcher3 last updated on 01/Sep/23
$$ \\ $$https://www.freebookcentre.net/maths-books-download/Exercises-and-Problems-in-Calculus.html
Commented by York12 last updated on 01/Sep/23
$${Thanks}\:{so}\:{much}\:{sir} \\ $$$${and}\:{I}\:{am}\:{still}\:{wondering}\:{if}\:{it}\:{would}\:{be}\: \\ $$$${possible}\:{to}\:{contact}\:{you} \\ $$
Commented by York12 last updated on 01/Sep/23
$$ \\ $$انا متشكر جداً جداً على هذا الموقع الرائع حضرتك اتمنى ان كان هناك مواقع او مصادر مشابهة ان تشاركها ان كان ممكناً و اتمنى ان كان بإمكاني التواصل مع حضرتك و اعدك ان لن ازعج حضرتك أبدا لكن كل ما في الأمر هو انه من النادر جداً ايجاد اشخاص مثلك متمكنين من للرياضيات خاصة في الوطن العربي
Commented by mr W last updated on 01/Sep/23
$${if}\:{he}\:{wants}\:{to}\:{be}\:{contacted},\:{he}\:{would} \\ $$$${have}\:{let}\:{you}\:{know}.\:{but}\:{he}\:{didn}'{t}\:{do}\:{this}, \\ $$$${that}\:{means}\:{he}\:{doesn}'{t}\:{want}\:{you}\:{to} \\ $$$${contact}\:{him}.\:{i}\:{think}\:{you}\:{should}\:{respect} \\ $$$${his}\:{decision}\:{and}\:{don}'{t}\:{ask}\:{him}\:{more} \\ $$$${about}\:{this}. \\ $$
Commented by York12 last updated on 01/Sep/23
$${I}\:{am}\:{not}\:{doing}\:{so}\:,\:{and}\:{if}\:{you}\:{do}\:{not} \\ $$$${have}\:{anything}\:{to}\:{help}\:{with}\:\:{then}\:{it}\:{would} \\ $$$${be}\:{better}\:{to}\:{stay}\:{silence}\:,\:{you}\:{do}\:{not} \\ $$$${know}\:{anything}\:{about}\:{me}\:{and}\:{by}\:{what} \\ $$$${you}\:{have}\:{said}\:{if}\:{he}\:{wants}\:{to}\:{contact} \\ $$$${me}\:{then}\:{he}\:{won}'{t},\:{I}\:{have}\:{asked}\:{for}\:{your} \\ $$$${help}\:{once}\:{and}\:{you}\:{were}\:{consistent}\:{not} \\ $$$${to}\:{help}\:{me}\:{with}\:{anything} \\ $$$${but}\:{remember} \\ $$$$ \\ $$
Commented by York12 last updated on 01/Sep/23
$$ \\ $$خيركم من تعلم العلم و علمه من كتم علما الجم يوم القيامة بلجام من نار
Commented by mr W last updated on 01/Sep/23
$${i}\:{didn}'{t}\:{help}\:{you},\:{not}\:{because}\:{i}\:{didn}'{t} \\ $$$${want}\:{to}\:{help},\:{but}\:{i}\:{can}'{t}\:{help}.\:{through} \\ $$$${your}\:{post}\:{above}\:{i}\:{realised}\:{that}\:{you} \\ $$$${actually}\:{don}'{t}\:{deserve}\:{any}\:{help},\:{also}\: \\ $$$${not}\:{from}\:{witcher}\mathrm{3}\:{sir}. \\ $$$${you}\:{constantly}\:{asked}\:{him}\:{to}\:{contact} \\ $$$${you},\:{but}\:{he}\:{kept}\:{silent}.\:{that}'{s}\:{saying} \\ $$$${that}\:{he}\:{has}\:{refused}\:{you}.\:{what}\:{is} \\ $$$${wrong}\:{when}\:{i}\:{friendly}\:{say}\:{that}\:{you}\: \\ $$$${should}\:{respect}\:{his}\:{decision}? \\ $$
Commented by York12 last updated on 01/Sep/23
$$ \\ $$لتقل خيرا او لتصمت
Commented by York12 last updated on 01/Sep/23
$${there}\:{is}\:{no}\:{problem}\:{with}\:{that}\:{but}\:{it}\:{does} \\ $$$${not}\:{help}\:{anymore}\:{and}\:{it}\:{is}\:{not}\:{beneficial} \\ $$$${and}\:{I}\:{think}\:{Witcher}\:{has}\:{something} \\ $$$${called}\:{langue}\:{he}\:{is}\:{not}\:{waiting}\:{for} \\ $$$${you}\:{to}\:{reply}\:{instead}\:{of}\:{him}\: \\ $$$${and}\:{you}\:{do}\:{not}\:{have}\:{any}\:{permission} \\ $$$${to}\:{do}\:{so}. \\ $$
Commented by York12 last updated on 01/Sep/23
$$ \\ $$$${And}\:{saying}\:{you}\:{did}\:{not}\:{help}\:{me} \\ $$$${does}\:{not}\:{mean}\:{you}\:{are}\:{a}\:{bad}\:{person} \\ $$$${but}\:{all}\:{what}\:{I}\:{am}\:{saying}\:{is}\:{since}\:{you} \\ $$$${can}\:{not}\:{help}\:{then}\:{do}\:{not}\:{put}\:{your}\:{nose} \\ $$$${in}\:{things}\:{which}\:\:{are}\:{non}\:{of}\:{your}\:{business} \\ $$$${or}\:{you}\:{will}\:{hear}\:{what}\:{you}\:{dislike} \\ $$$${And}\:{I}\:{am}\:{repeating}\:{again}\:{no}\:{one} \\ $$$${called}\:{you}\:{out}\:{to}\:{speak}\:{instead}\:{of}\:{him}. \\ $$$$ \\ $$$$ \\ $$
Commented by York12 last updated on 01/Sep/23
$$ \\ $$and for saying I don't deserve any help, I don't care cause you aren't the one who can judge that and I don't need any kind of help from you and anyway you yourself said you didn't help because you don't have the capability to help and me too I think you don't deserve to be helped in any way cause you don't hope good things for others, you have a stupid mentality which makes you think that when you prevent the knowledge from others then you will be above all of them which is a complete trash mentality cause there are billions of people who are better than you who are ready to help and If you won't help then okay someone else can help and you don't have the permission to prevent others from doing so okay, have a good time my dear :)))
Commented by York12 last updated on 01/Sep/23
$$ \\ $$And to make sure you won't interpret what I have said as you want, I am saying again Yeah you didn't say any wrong thing but basically you don't have the permission to speak instead of him , add above that what you have said doesn't help me neither him, he can simply tell me the same thing you have said, finally it not only not helping but would make him change his mind about contacting me and I have the right to think you are trying to do so cause your action doesn't have any logical reason to send such a message
Commented by York12 last updated on 02/Sep/23
$$ \\ $$And yes, I was about to forget to mention that we both come from the same country, speak the same language, share the same religion, have the same culture, and similar ways of thinking. While you are a foreign atheist who knows nothing about us, this is like outsiders interfering in a family's matters. It's better for you to stay completely away. My conversations are not based on the backward ethics of foreigners, which are not ethics or principles at all; they are based on interests, immorality, and corruption. If you don't want to talk to me, I can convince you with our ethics, not the ethics of animals in the decaying Western civilization that allows everything under the guise of freedom, which is essentially servitude to the arrogant elites in your collapsing civilization built on the theft of other nations' wealth, selling alcohol, drugs, and cheap, flashy products. Do you understand, foreigner? Stay away. What you don't know about us is that withholding knowledge in our country is considered a crime, not freedom. Withholding knowledge leads to decline, while sharing it leads to progress. I don't like that you don't understand this fundamental principle. You have a backward mentality, making you believe that when you prevent others from acquiring knowledge, you will be superior, and they will know nothing. But this is not true; you are not the source of all knowledge. You are not the gatekeeper. If someone knocks on a door and it doesn't open, there are many doors in life. God gives and opens doors, and He is the creator of all knowledge, holding everything in His hands. This is everything, my atheist friend.
Commented by York12 last updated on 02/Sep/23
$$ \\ $$و من علامة اعراض الله عن العبد ان يجعل شغله فيما لا يعنيه