Let bn sinpin8 for n gt 0 use partial fractions to rewrite

Question

1. Let a_n = (-1)ⁿ, compute lim_n→∞a_n.

2. Let b_n = sin(πn/8), for n > 0.

• Compute the limit of a_n.
• Let s_n be the sum of first n elements of a_n. That is, s_n = _i=1∑ⁿ a_n. Write out the first 8 element of s_n.
• Use partial fractions to rewrite a_n as the sum of two fractions.
• Find a closed from expression for s_n.
• Using your expression for s_n, compute lim_n→∞ s_n. What is _n=1∑^∞ a_n?