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(1/(((√1)+(√2))((1)^(1/(4 )) +(2)^(1/(4 )) ))) + (1/(((√2)+(√3))((2)^(1/( 4)) +(3)^(1/(4 )) ))) + (1/(((√3)+(√4))((3)^(1/(4 )) +(4)^(1/(4 )) ))) + ... + (1/(((√(255))+(√(256)))(((255))^(1/(4 )) +((256))^(1/(4 )) ))) = ...

$$\frac{\mathrm{1}}{\left(\sqrt{\mathrm{1}}+\sqrt{\mathrm{2}}\right)\left(\sqrt[{\mathrm{4}\:}]{\mathrm{1}}+\sqrt[{\mathrm{4}\:}]{\mathrm{2}}\right)}\:+\:\frac{\mathrm{1}}{\left(\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}\right)\left(\sqrt[{\:\mathrm{4}}]{\mathrm{2}}+\sqrt[{\mathrm{4}\:}]{\mathrm{3}}\right)}\:+ \\ $$$$\frac{\mathrm{1}}{\left(\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}\right)\left(\sqrt[{\mathrm{4}\:}]{\mathrm{3}}+\sqrt[{\mathrm{4}\:}]{\mathrm{4}}\right)}\:+\:...\:+\:\frac{\mathrm{1}}{\left(\sqrt{\mathrm{255}}+\sqrt{\mathrm{256}}\right)\left(\sqrt[{\mathrm{4}\:}]{\mathrm{255}}+\sqrt[{\mathrm{4}\:}]{\mathrm{256}}\right)} \\ $$$$=\:...\: \\ $$

Question Number 83910 Answers: 2 Comments: 1

find all 6 digit numbers which are not only palindrome but also divisible by 495.

$$\mathrm{find}\:\mathrm{all}\:\mathrm{6}\:\mathrm{digit}\:\mathrm{numbers}\:\mathrm{which}\:\mathrm{are}\:\mathrm{not} \\ $$$$\mathrm{only}\:\mathrm{palindrome}\:\mathrm{but}\:\mathrm{also}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{495}. \\ $$

Question Number 83899 Answers: 0 Comments: 1

Defined a function f(x) such that f(1−x)+2f(x)= nx for m ,n > 1 , the value of ∫ _1 ^( m) (2n+6f((m/x))) dx is ...

$$\mathrm{Defined}\:\mathrm{a}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{such}\: \\ $$$$\mathrm{that}\:\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)+\mathrm{2f}\left(\mathrm{x}\right)=\:\mathrm{nx}\: \\ $$$$\mathrm{for}\:\mathrm{m}\:,\mathrm{n}\:>\:\mathrm{1}\:,\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\int\underset{\mathrm{1}} {\overset{\:\mathrm{m}} {\:}}\left(\mathrm{2n}+\mathrm{6f}\left(\frac{\mathrm{m}}{\mathrm{x}}\right)\right)\:\mathrm{dx}\:\mathrm{is}\:... \\ $$

Question Number 83898 Answers: 0 Comments: 4

∫(du/((√(u^2 −1 ))−u))

$$\int\frac{\mathrm{du}}{\sqrt{\mathrm{u}^{\mathrm{2}} −\mathrm{1}\:}−\mathrm{u}} \\ $$

Question Number 83893 Answers: 0 Comments: 1

∫(du/(u−u^2 ))

$$\int\frac{\mathrm{du}}{\mathrm{u}−\mathrm{u}^{\mathrm{2}} } \\ $$

Question Number 83886 Answers: 0 Comments: 15

To the developers of TinkuTara: problem 1: i get no notifications when my posts are updated. problem 2: i can edit my post, see picture 1, but the content is not visiable, see picture 2.

$${To}\:{the}\:{developers}\:{of}\:{TinkuTara}: \\ $$$${problem}\:\mathrm{1}: \\ $$$${i}\:{get}\:{no}\:{notifications}\:{when}\:{my}\:{posts} \\ $$$${are}\:{updated}. \\ $$$$ \\ $$$${problem}\:\mathrm{2}: \\ $$$${i}\:{can}\:{edit}\:{my}\:{post},\:{see}\:{picture}\:\mathrm{1},\:{but} \\ $$$${the}\:{content}\:{is}\:{not}\:{visiable},\:{see}\:{picture}\:\mathrm{2}. \\ $$

Question Number 83935 Answers: 0 Comments: 0

If x^4 and higher powers of x are neglected, show that (√((((1−x)/(1+x+x^2 )))=1−x+(1/2)x^3 ))

$${If}\:\:\boldsymbol{{x}}^{\mathrm{4}} \:{and}\:{higher}\:{powers}\:{of}\:{x}\:{are}\:{neglected},\:{show}\:{that} \\ $$$$\sqrt{\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}+{x}^{\mathrm{2}} }\right)=\mathrm{1}−{x}+\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{3}} } \\ $$

Question Number 83876 Answers: 0 Comments: 0

Question Number 83874 Answers: 1 Comments: 1

Question Number 83871 Answers: 0 Comments: 4

If equation { (((√(x^2 +y^2 ))+(√((x−4)^2 +y^2 ))+(√(x^2 +(y−3)^2 ))+(√((x−4)^2 +(y−3)^2 ))=10)),((x+2y= 5z)) :} has solution is (a,b,c). find a+2b+3c

$$\mathrm{If}\:\mathrm{equation}\: \\ $$$$\begin{cases}{\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }+\sqrt{\left(\mathrm{x}−\mathrm{4}\right)^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }+\sqrt{\mathrm{x}^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{3}\right)^{\mathrm{2}} }+\sqrt{\left(\mathrm{x}−\mathrm{4}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{3}\right)^{\mathrm{2}} }=\mathrm{10}}\\{\mathrm{x}+\mathrm{2y}=\:\mathrm{5z}}\end{cases} \\ $$$$\mathrm{has}\:\mathrm{solution}\:\mathrm{is}\:\left(\mathrm{a},\mathrm{b},\mathrm{c}\right).\: \\ $$$$\mathrm{find}\:\mathrm{a}+\mathrm{2b}+\mathrm{3c}\: \\ $$

Question Number 83865 Answers: 0 Comments: 3

lim_(x→−∞ ) (x(√(2x+2))−x(√(2x+3)))

$$\underset{{x}\rightarrow−\infty\:} {\mathrm{lim}}\:\left(\mathrm{x}\sqrt{\mathrm{2x}+\mathrm{2}}−\mathrm{x}\sqrt{\mathrm{2x}+\mathrm{3}}\right) \\ $$

Question Number 83864 Answers: 0 Comments: 3

what Maclaurin series of function tan (x)?

$$\mathrm{what}\:\mathrm{Maclaurin}\:\mathrm{series}\:\mathrm{of}\:\mathrm{function} \\ $$$$\mathrm{tan}\:\left(\mathrm{x}\right)? \\ $$

Question Number 83861 Answers: 0 Comments: 3

An object of mass 7kg is sliding down a frictionless 20m inclined plane. Calculate the speed of the object when it reaches the ground.

$$\mathrm{An}\:\mathrm{object}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{7kg}\:\mathrm{is}\:\mathrm{sliding}\:\mathrm{down} \\ $$$$\mathrm{a}\:\mathrm{frictionless}\:\mathrm{20m}\:\mathrm{inclined}\:\mathrm{plane}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{object}\:\mathrm{when}\: \\ $$$$\mathrm{it}\:\mathrm{reaches}\:\mathrm{the}\:\mathrm{ground}. \\ $$

Question Number 83859 Answers: 0 Comments: 1

lim_(x→0) ((1/x^2 )− cot^2 x)= ?