Show that $ (\sum_{i=1}^n x_iy_i)^2\leq \sum_{i=1}^n x_i^2\sum_{i=1}^n y_i^2 $ with induction
95030
Proving the Cauchy-Schwarz inequality by induction
80556
Demonstrate by induction the inequality: $\ln(1+n)\leq\sum_{i=1}^{n}\frac{1}{i}\leq1+\ln(n)$
68308
A (probably trivial) induction problem: $\sum_2^nk^{-2}\lt1$
93427
Show that $\sum_{i=1}^{n} \frac {a_i}{1+a-a_i} + \prod_{i=1}^{n} {(1-a_i)} \leq 1$
36639
Prove by induction that $\sum_{r=0}^{n}\begin{pmatrix}n \\ r \end{pmatrix}=2^k$
119436
Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction
52113
Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$
135807
I'm having trouble with a proof by induction
17157
Proving $\sum\limits_{k=1}^{n}{\frac{1}{\sqrt{k}}\ge\sqrt{n}}$ with induction
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
73938
Prove that $\sum_{r=1}^nr(r+1)=\frac{n(n+1)(n+2)}{3}$ using induction
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction
125028
Prove the following equality using mathematical induction:
62177
Prove that: $2^n < n!$ Using Induction
115912
Summation inductional proof: $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\ldots+\frac{1}{n^2}<2$
146200
proof by induction: sum of binomial coefficients $\sum_{k=0}^n (^n_k) = 2^n$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$