- #1

Potatochip911

- 318

- 3

## Homework Statement

Prove:

*Hint:*Group the terms in the error as ##(a_{n+1}+a_{n+2})+(a_{n+3}+a_{n+4})+\cdots## to show that the error has the same sign as ##a_{n+1}##. Then group them as ##a_{n+1}+(a_{n+2}+a_{n+3})+(a_{n+4}+a_{n+5})+\cdots## to show that the error has magnitude less than ##\left| a_{n+1} \right |##.

## Homework Equations

3. The Attempt at a Solution [/B]

From the first part of the hint I can see that the grouped terms ##(a_{n+1}+a_{n+2})+\cdots## will take the sign of the first term because ##\lim_{n\to\infty}a_{n}=0## therefore, ##\left | \lim_{n\to\infty}a_{n+1} \right | > \left | \lim_{n\to\infty}a_{n+2} \right | ## At this point I am not really sure what to do with the second part of the hint although I'm assuming it has something to do with the less than or equal to symbol.

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