proof of $1^4+2^4+...+n^4=\frac{n(n+1)(2n+1)(3n^2+3n-1)}{30}$
69679
Geometric interpretation for sum of fourth powers
81136
Prove by induction that... $1+3+5+7+...+(2n+1)=(n+1)^2$ for every $n \in \mathbb N$
123820
Guess the formula for $\sum\frac 1{(4n-3)(4n+1)}$ and prove by induction
73002
For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$
10629
How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction
17100
Prove that $\frac{b^2+c^2}{b+c}+\frac{c^2+a^2}{c+a}+\frac{a^2+b^2}{a+b} \ge a+b+c$
112907
Math Induction Proof: $(1+\frac1n)^n < n$
131771
Prove by induction that $\sum_{i=1}^{2^n} \frac{1}{i} \ge 1+\frac{n}{2}, \forall n \in \mathbb N$
142715
Manipulating expression $(\frac{1}{4}+\frac{1}{2^{n+1}})(1-\frac{1}{2^{n+1}})$ in inductive step.
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} $
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 $F_{2n} = F^2_{n+1} - F^2_{n-1}$
2675
Proof $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$
105164
If $abc=1$, prove that $\frac{2}{(a+1)^2+b^2+1} + \frac{2}{(b+1)^2+c^2+1} + \frac{2}{(c+1)^2+a^2+1} \le 1$.
48503
Proving : $ \bigl(1+\frac{1}{n+1}\bigr)^{n+1} \gt (1+\frac{1}{n})^{n} $
61859
Prove $\sum \frac{a}{a+b^4+c^4} \le 1$
70625
Prove By Induction $1 + 1/2 + 1/3 + ... + 1/(2^n) ≥ 1 + n/2$