Find the sum of the series

Question

Find the sum of the series  correct to four decimal places.

Type your answer in the space below and give 4 decimal places. If your answer is less than 1, place a leading "0" before the decimal point (ex: 0.4812).

Answer 1

0.9727

from just calculating the first 5 terms of the series

n=1 partial sum = 1

n=2 partial sum = 1-1/32 = 1-0.03125 = 0.96875

n=3 partial sum = 1-1/32 + 1/243 = 0.96875+0.00412 = 0.9728

n=4 partial sum = 0.9728 - 1/256 = 0.9728- 0.00039 = 0.9724

n=5 5th term = 1/5^5 = 1/3125 = 0.0003

partial sum = 0.9724 + 0.0003 = 0.9727

n=6 6th term = 1/6^5 = too small to matter for 4 decimal places