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Question Number 103510 Answers: 1 Comments: 5

Question Number 103504 Answers: 0 Comments: 0

Question Number 103503 Answers: 2 Comments: 0

Solve : 3^x = 4x

$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:{Solve}\:: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{3}^{{x}} \:=\:\mathrm{4}{x} \\ $$

Question Number 103236 Answers: 0 Comments: 3

e^e^(e.....∞) =?

$${e}^{{e}^{{e}.....\infty} } =? \\ $$

Question Number 103219 Answers: 1 Comments: 3

1+1+1+1+1+1+1+....=S_n S_n =1+1+1+1+1+1+1+.... 2S_n = 2 + 2 + 2+....... .......... subtracting −S_n =1−1+1−1+1−1+1−1+1−1+.... −S_n =(1/2) S_n =−(1/2) I have found this while experiment . I know the sum diverges but is it pretty cool? Kindly rectify me if there is any fault on this non rigorous process I have found some Ramanujan proof S_n =1+2+3+4+5+6+7+... 4S_n = 4+ 8 + 12+... −3S_n =1−2+3−4+5−6+7−8+...... −3S_n =(1/4) S_n =−(1/(12)) Ramanujan had done this on his notebook

Question Number 103209 Answers: 3 Comments: 0

Question Number 103119 Answers: 0 Comments: 0

∫((log(((1+(√5))/2)(√x)−1))/(x^(√x) log(((1+(√5))/2)(√x)+1)−1))

$$\int\frac{{log}\left(\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\sqrt{{x}}−\mathrm{1}\right)}{{x}^{\sqrt{{x}}} {log}\left(\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\sqrt{{x}}+\mathrm{1}\right)−\mathrm{1}} \\ $$

Question Number 103016 Answers: 0 Comments: 0

Question Number 103859 Answers: 1 Comments: 0

solve : y^2 + x^2 = −sin(θ) ., (π/2)≥ θ≥−(π/2)

$$\:\:\: \\ $$$$\:\:\:\:\:\:{solve}\:: \\ $$$$\:\:\:\:\:\:{y}^{\mathrm{2}} \:+\:{x}^{\mathrm{2}} \:=\:−\mathrm{sin}\left(\theta\right)\:\:\:\:\:.,\:\:\:\:\frac{\pi}{\mathrm{2}}\geqslant\:\theta\geqslant−\frac{\pi}{\mathrm{2}} \\ $$

Question Number 102822 Answers: 1 Comments: 1

Σ_(n=1) ^∞ ((n!)/n^n )

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}!}{{n}^{{n}} } \\ $$

Question Number 102745 Answers: 0 Comments: 2

1−1+1−1+1−1+1−1+.....=(1/2) {But it diverges 1+1+1+1+1+1+1+......=−(1/2) {But it diverges 1+2+4+8+16+.....=−1 {But it diverges 1+2+3+4+5+6+7=−(1/(12)) {But it diverges 1−2+4−8+.....=(1/3) {But it diverges 1−2+3−4+5−6+.....=(1/4) {Is it a divergent?????

$$\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+.....=\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+......=−\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{4}+\mathrm{8}+\mathrm{16}+.....=−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}=−\frac{\mathrm{1}}{\mathrm{12}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}−\mathrm{2}+\mathrm{4}−\mathrm{8}+.....=\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}−\mathrm{2}+\mathrm{3}−\mathrm{4}+\mathrm{5}−\mathrm{6}+.....=\frac{\mathrm{1}}{\mathrm{4}}\:\:\:\:\:\:\:\left\{{Is}\:{it}\:{a}\:{divergent}?????\right. \\ $$

Question Number 102701 Answers: 2 Comments: 1

Evaluate: ∫((sin x)/x)dx

$${Evaluate}: \\ $$$$\int\frac{\mathrm{sin}\:{x}}{{x}}{dx} \\ $$

Question Number 102686 Answers: 0 Comments: 1

Σ_(r=1) ^∞ i^r +Σ_(r=0) ^∞ i^r

$$\underset{{r}=\mathrm{1}} {\overset{\infty} {\sum}}{i}^{{r}} +\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}{i}^{{r}} \\ $$

Question Number 102664 Answers: 2 Comments: 0

2x=5 x=? −−− for test app only

$$\mathrm{2}{x}=\mathrm{5} \\ $$$${x}=? \\ $$$$−−− \\ $$$$\boldsymbol{{for}}\:\boldsymbol{{test}}\:\boldsymbol{{app}}\:\boldsymbol{{only}} \\ $$

Question Number 102651 Answers: 0 Comments: 1

12+14+24+58+164....upto nth terms

$$\mathrm{12}+\mathrm{14}+\mathrm{24}+\mathrm{58}+\mathrm{164}....\mathrm{upto}\:\mathrm{nth}\:\mathrm{terms} \\ $$

Question Number 102635 Answers: 2 Comments: 0

Question Number 102627 Answers: 3 Comments: 0

show that: cosθ + cos2θ + ....cos nθ= ((cos (1/2)(n +1)θ sin(1/2)nθ)/(sin (1/2)nθ)) Show that: sin θ + sin 2θ + ....+ sin nθ = ((sin (1/2)(n + 1)θ sin(1/2)nθ)/(sin (1/2)nθ)) where θ ∈ R and θ ≠2πk , k ∈Z

$$\mathrm{show}\:\mathrm{that}:\:\mathrm{cos}\theta\:+\:\mathrm{cos2}\theta\:+\:....\mathrm{cos}\:{n}\theta=\:\frac{\mathrm{cos}\:\frac{\mathrm{1}}{\mathrm{2}}\left({n}\:+\mathrm{1}\right)\theta\:\mathrm{sin}\frac{\mathrm{1}}{\mathrm{2}}{n}\theta}{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{n}\theta} \\ $$$$\mathrm{Show}\:\mathrm{that}:\:\mathrm{sin}\:\theta\:+\:\mathrm{sin}\:\mathrm{2}\theta\:+\:....+\:\mathrm{sin}\:{n}\theta\:=\:\frac{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}\left({n}\:+\:\mathrm{1}\right)\theta\:\mathrm{sin}\frac{\mathrm{1}}{\mathrm{2}}{n}\theta}{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{n}\theta} \\ $$$$\mathrm{where}\:\theta\:\in\:\mathbb{R}\:\mathrm{and}\:\theta\:\neq\mathrm{2}\pi{k}\:,\:{k}\:\in\mathbb{Z} \\ $$$$ \\ $$

Question Number 102598 Answers: 2 Comments: 0

Question Number 102545 Answers: 1 Comments: 0

Question Number 102544 Answers: 2 Comments: 0

Question Number 102539 Answers: 3 Comments: 2

2+3.3+4.3^2 +5.3^2 +.....up to n terms

$$\mathrm{2}+\mathrm{3}.\mathrm{3}+\mathrm{4}.\mathrm{3}^{\mathrm{2}} +\mathrm{5}.\mathrm{3}^{\mathrm{2}} +.....{up}\:{to}\:{n}\:{terms} \\ $$

Question Number 102530 Answers: 0 Comments: 1

Question Number 102484 Answers: 1 Comments: 0

Question Number 102407 Answers: 0 Comments: 0

Sir MJS & Sir John Santu You both have decided to leave this forum for different reasons. Being agree with your reasons and accepting your right of decision I dare to suggest not to disconnect fully from the forum.Please stay connected although for very short time on daily/weekly basis.This is also necessary because we have no means to contact you. After all this is only a request. You may or may not accept it.

$$\mathrm{Sir}\:\mathrm{MJS}\:\&\:\mathrm{Sir}\:\mathrm{John}\:\mathrm{Santu} \\ $$$${You}\:{both}\:{have}\:{decided}\:{to}\:{leave} \\ $$$${this}\:{forum}\:{for}\:{different}\:{reasons}. \\ $$$${Being}\:{agree}\:{with}\:{your}\:{reasons} \\ $$$${and}\:{accepting}\:{your}\:{right}\:{of}\: \\ $$$${decision}\:{I}\:{dare}\:{to}\:{suggest}\:{not} \\ $$$${to}\:{disconnect}\:{fully}\:{from}\:{the} \\ $$$${forum}.{Please}\:{stay}\:{connected} \\ $$$${although}\:{for}\:{very}\:{short}\:{time}\:{on} \\ $$$${daily}/{weekly}\:{basis}.\mathcal{T}{his}\:{is}\:{also} \\ $$$${necessary}\:{because}\:{we}\:{have}\:{no} \\ $$$${means}\:{to}\:{contact}\:{you}. \\ $$$$\:\:\:\:\mathcal{A}{fter}\:{all}\:{this}\:{is}\:{only}\:{a}\:{request}. \\ $$$${You}\:{may}\:{or}\:{may}\:{not}\:{accept}\:{it}. \\ $$$$ \\ $$

Question Number 102362 Answers: 0 Comments: 0

please how calculate the development limity of f(x,y)=x^y ,take a( 3,2) at order one and two

$${please}\:{how}\:{calculate}\:{the}\:{development}\:\:{limity}\:{of}\:{f}\left({x},{y}\right)={x}^{{y}} \\ $$$$\:,{take}\:{a}\left(\:\mathrm{3},\mathrm{2}\right)\:{at}\:{order}\:{one}\:{and}\:{two} \\ $$

Question Number 102336 Answers: 1 Comments: 1

if f(x)≤2l +1 and ∫_1 ^3 f(x)dx≤l^2 find the value of l

$${if}\:\:{f}\left({x}\right)\leqslant\mathrm{2}{l}\:+\mathrm{1}\: \\ $$$${and}\:\:\int_{\mathrm{1}} ^{\mathrm{3}} {f}\left({x}\right){dx}\leqslant{l}^{\mathrm{2}} \\ $$$${find}\:{the}\:{value}\:{of}\:{l} \\ $$

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