Determine how many terms of the following convergent series must be summed to be sure that the remainder is less than 10 Superscript negative 5 in magnitude. Summation from k equals 1 to infinity StartFraction (negative 1 )Superscript k plus 1 Over k cubed EndFraction

You need to sum at least 5000 terms

Step-by-step explanation:

Remember what the estimation theorem for alternating series says.

Given a series

An upper bound for the error of the series  is so

For this case you want

is approximately 5000. So you must sum at least 5000 terms.