Question

Determine how many terms should be used to estimate the sum of the entire series with an error of less than 0.001.

Answer 1

Answer: 9

Explanation:

Tₙ ₊ ₁ < 0.001

1 / ( (n+1) 3 +1 ) < 0.001

(n+1)3 + 1 > 1000

(n+1)3 > 999

n+1 > 9.9966

n = 8.9966 => n = 9

I should take n = 9 to be sure that the error is less than 0.001.