Easy way to prove $\frac{2^n+1}{5^n+1}\gt\frac{2^n}{5^n}$ for all $n\gt0$
102420
How to prove that adding $n$ to the numerator and denominator will move the resultant fraction close to $1$?
84147
Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
24469
Prove $ 2<(1+\frac{1}{n})^{n}$
25054
Proving $\frac{1}{n+1} + \frac{1}{n+2}+\cdots+\frac{1}{2n} > \frac{13}{24}$ for $n>1,n\in\Bbb N$ by Induction
96700
How is $\dfrac1{(1-x)^5}=\sum_{n\geq0}{n+4\choose4}x^n$
91000
Prove that $\frac{1}{a+1}0$
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
118140
Prove that $ \frac{n(n-1)(n-k+1)}{k(k-1)\cdots1} = \frac{n!}{(n-1)!k!}$
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
150642
How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
125618
Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction
59475
Show that $\sqrt{n+1}-\sqrt{n}\to0$
21826
How to prove $\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
50599
Prove that $\frac{1}{1*3}+\frac{1}{3*5}+\frac{1}{5*7}+...+\frac{1}{(2n-1)(2n+1)}=\frac{n}{2n+1}$
102531
Prove $\sum\limits^m_{k=0} \frac{2n-k\choose k}{2n-k\choose n}\frac{2n-4k+1}{2n-2k+1}2^{n-2k}=\frac{n\choose m}{2n-2m\choose n-m}2^{n-2m}$ for-