Mathematical Induction proof that $\sum\limits_{i=1}^n \frac{1}{i^2} < 2 - \frac1n$
136737
Proof by Induction for inequality, $\sum_{k=1}^nk^{-2}\lt2-(1/n)$
27580
Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$
133331
Proof by induction: $\sum\limits_{i=1}^{n} \frac{1}{n+i} = \sum\limits_{i=1}^{n} \left(\frac{1}{2i-1} - \frac{1}{2i}\right)$
66568
Number Theory : Show that $\sum_{i=0}^\infty$ $ [\frac{n}{2^i}+\frac{1}{2}]$ $=$ $2n$
123820
Guess the formula for $\sum\frac 1{(4n-3)(4n+1)}$ and prove by induction
52113
Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$
130093
Prove by Induction : $n < 2^n$
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
86348
Proving $\sum\limits_{k=0}^{n-1} \Bigl[x + \frac{k}{n}\Bigr] = [nx]$
63652
Mathematical induction for inequalities: $\frac1{n+1} + \frac1{n+2} + \cdots +\frac1{3n+1} > 1$
108596
Proof by induction for "sum-of"
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
11407
Proving the summation formula using induction: $\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$
78583
Help with proof using induction: $1 + \frac{1}{4} + \frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
24469
Prove $ 2<(1+\frac{1}{n})^{n}$
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$