# Induction proof

ptolema

## Homework Statement

prove that
using induction

hint: use induction on n, and compare derivatives

## Homework Equations

P(n) says "1+x+x2/2!+...+xn/n!"
P(1)=1+x1/1!=1+x so P(1) is true

## The Attempt at a Solution

induction is probably my worst type of proof, i can't wrap my head around how to do it. apparently there is some some taylor series that goes with this, but we haven't done those yet. can someone please help?

icystrike
Start from p(1) .

What is the value on left hand side?

What is the value on right hand side if you sum the first 4 terms?

After proving it is true.. assume p(n) is true such that n is an element of non-negative integers.

hence proving p(n+1) is true by the assumption that p(n) is true.

Hint: $$(n+1)^{k}\ge n^{k}$$ for k:{1,2,3,4,...,n}