Find the sum of the series the series from n equals 1 to infinity of the quotient of negative 1 raised to the n minus 1 power and n squared correct to two decimal places.

Question

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



Type your answer in the space below and give 2 decimal places.

Answer 1

Try calculating the first 10 or 11 terms

1/1 -1/4 + 1/9 -1/16 + 1/25 -1/36 +1/49 -1/64 +1/81 -1/100 + 1/121 = 0.825962 or round off to 0.83

the 12th through infinite terms may change it but it hovers around 0.825, could go either way to 0.83 or 0.82 for two decimal places.

Calculate a few more terms if you want, 13, 14, 15, convert them to decimals and sum them.

pi^2/12 = 0.8224656644....

Answer 2

This is a well known series: ∑ = π²/12 ≈ 0.82