Rajesh K Singh
Reputation
1,280
Next privilege 2,000 Rep.
4 25
Impact
~40k people reached

• 0 posts edited

### Questions (99)

 20 If $a$, $a+2$ and $a+4$ are prime numbers then, how can one prove that there is only one solution for $a$? 8 Integrating $\int_0^\infty\frac{1}{1+x^6}dx$ 7 factorise, $x^3-13x^2+32x+20$ 7 Prove that $(n+\sqrt{n^2 -1})^k$ will always be of the form$(t+\sqrt{t^2 -1})$ where $n$, $k$, $t$ are natural numbers 5 how can one solve for $x$, $x =\sqrt{2+\sqrt{2+\sqrt{2\cdots }}}$ [duplicate]

### Reputation (1,280)

 +5 what is the new order of the digits here ? Both the numbers $144$ and $441$ consists of the same digits? +5 what is the value of $\int_{-1}^{1}\frac{1}{x^n}dx$, x is a natural number. +5 Is $7^{6n}-6^{6n}$ always divisible by $13$,$127$ and $559$, for any natural number $n$? -2 How do we prove that the Pythagorean theorem holds for a right angled isoceles triangle with sides, $a,b,a$.

 3 What is the remainder when $25^{889}$ is divided by 99? 2 Integrating $\int \sqrt{\frac{1+x}{x}}dx$ 2 I know that, $S_{2n}+4S_{n}=n(2n+1)^2$. Is there a way to find $S_{2n}$ or $S_{n}$ by some mathematical process with just this one expression? 2 how can one solve for $x$, $x =\sqrt{2+\sqrt{2+\sqrt{2\cdots }}}$ 2 How to integrate $\frac{1}{\sqrt{1+x^2}}$ using substitution?

### Tags (75)

 5 algebra-precalculus × 23 2 proof-strategy × 2 5 elementary-number-theory × 14 2 divisibility 3 integration × 13 1 functions × 9 3 recurrence-relations × 4 1 differential-equations × 8 2 nested-radicals × 2 1 circle × 3

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