Induction: Show: $\frac{1}{2} \times \frac{3}{4} \times \frac{5}{6} \times ... \times \frac{2n-1}{2n} \leq \frac{1}{\sqrt{3n+1}}$
7404
Induction and convergence of an inequality: $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\leq \frac{1}{\sqrt{2n+1}}$
87941
Prove by mathematical induction that $\forall n \in \mathbb{N} : \sum_{k=1}^{2n} \frac{(-1)^{k+1}}{k} = \sum_{k=n+1}^{2n} \frac{1}{k} $
80556
Demonstrate by induction the inequality: $\ln(1+n)\leq\sum_{i=1}^{n}\frac{1}{i}\leq1+\ln(n)$
158210
showing $\arctan(\frac{2}{3}) = \frac{1}{2} \arctan(\frac{12}{5})$
16812
Proving $1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ using induction
63474
Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?
73191
Proving that $\frac{1}{1\cdot 2} + \frac{1}{2\cdot 3} + \frac{1}{3 \cdot 4} +\ldots + \frac{1}{n(n+1)} = \frac{n}{n+1}$
125040
Show by induction : $n^7-n$ is a multiple of 7
108698
proof using the mathematical induction
96332
Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$
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: $\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$
148330
Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
27580
Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$
81842
How to prove by induction that $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$?
19701
Prove $5\mid2^{4n}-1$ by induction
65315
Showing $1+2+\cdots+n=\frac{n(n+1)}{2}$ by induction (stuck on inductive step)