Prove by induction that ∣z1+z2+⋯+zn∣≤∣z1∣+∣z2∣+⋯+∣zn∣ for all n∈ℕ n N .
93599
General Proof for the triangle inequality
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} $
123195
Prove by induction that a^n+a^-n is an integer.
62747
Use induction to prove a product of sums of squares is a sum of squares
27304
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
130093
Prove by Induction : $n < 2^n$
65315
Showing $1+2+\cdots+n=\frac{n(n+1)}{2}$ by induction (stuck on inductive step)
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
125297
Induction to prove $2n + 3 < 2^n$
150462
Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$
71451
A proof by strong induction that $a_n\le3^n$ where $a_n=a_{n-1}+a_{n-2}+a_{n-3}$
65391
Prove by induction. $n \in \mathbb N$.
71650
Proving by strong induction for a sequence of integers, $2^n$ divides term $n$
76696
Using induction to prove $2^{n-1}(1 + a_1a_2\ldots a_n) \geq (1+a_1)(1+a_2)\ldots(1+a_n)$ for $a_i \geq 1$
41784
Prove using mathematical induction that $n < 3 ^n$ for all positive integers n.