# MTH 251 Lecture Notes - Lecture 32: Squeeze Theorem, Ratio Test

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15 May 2018

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Lecture Notes

Tn is the degree Taylor polynomial of at .

Setting where is called the remainder of the Taylor series

If we can show that

Then we have:

Theorem:

If

Where is the nth degree Taylor polynomial and

then is the sum of the

Taylor series on the internal where is the radius of convergence and a is the

center.

Two useful things

Taylor’s Inequality

for then the

for

Also,

for all

Back to :

If then is

For all

Then, for

Then, by Taylor’s inequality,

For

Now notice that,

By squeeze theorem,