Induction proof

  • Thread starter ptolema
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  • #1
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Homework Statement



prove that
taylorseries.jpg
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?
 

Answers and Replies

  • #2
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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: [tex](n+1)^{k}\ge n^{k}[/tex] for k:{1,2,3,4,...,n}
 

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