Question

determine how many terms we need to add in order to find the sum with an error less than 0.0001. If the quantity

Answer 1

The answer is "
`n \geq 9` and
`error < 10^(-4)`".

Explanation:

`\sum_(n=1)^(\infty) (-1^n)/(n 2^n)\\\\`

Error after
`n^(th)`term:

`|R_n|= |((-1)^(n+1))/((n+1) 2^(n+1))| = (1)/((n+1)2^(n+1))\\\\\to (1)/((n+1)2^(n+1)) < 0.0001\\\\\to 10000< 2^(n+1) (n+1)\\\\\to n\geq 9 \ \ \text{satisfies the inequality}\\\\\to error< 10^(-4)\\`