Question

problem 1and 2

Problem 1 [3 marks] Assume that the nth term in the sequence of partial sums for the series ,, is given below. Determine if the series is convergent or divergent. If the series is convergent determine the value of the series. a) Sn = 2-72 b) SEP Problem 2 [2 marks] Does the series (-1)" cos converge absolutely, or diverge?

Answer 1

SOLUTION :

a.

Sn = (5 + 8n^2) / (2 - 7n^2) = (5/n^2 + 8) / (2/n^2 - 7)

Limit n -> ∞ , Sn = (0 + 8) / (0 - 7) = - 8/7 

So, it is convergent and value is - 8/7 (ANSWER)

b.

Sn = n^2 / (5 + n) = (n^2/n^2) / (5/n^2 + n/n^2) = 1 /  (5/n^2 + 1/n)

Limit n -> ∞ , Sn = 1 / (0 + 0)) = 1 / 0 = ∞ 

So, it is divergent and value is ∞ (ANSWER)

Answer 2