Question

Is the answer to my first question right? I am having trouble with the second one, so I have no answer, if you could please help me.

Answer 1

Answer:

Absolutely convergent

0.82

Step-by-step explanation:

Use the alternating series test.

lim(n→∞) (1/√n) = 0

1/√n > 1/√(n+1) for n > 0

It is absolutely convergent.

Use error estimation.

1/(n+1)² < 0.01

(n+1)² > 100

n+1 > 10

n > 9

n = 10

Sum the first 10 terms.

∑₁¹⁰ (-1)ⁿ⁻¹/n²

= 1/1² − 1/2² + 1/3² − 1/4² + 1/5² − 1/6² + 1/7² − 1/8² + 1/9² − 1/10²

≈ 0.82