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

User Zeroin
by
8.9k points

1 Answer

7 votes

Answer:

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)\\

User Jurn
by
9.3k points

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