1. For each of the following, find an explicit formula for the nth term of the series: n k+1 (a) G₁ = (2) -£*** (b) Gn =0 -Στ() n k (c) Α = Σ (5 -Σ(-) k=0 n m (α) 5η = ΣΣΕ m=1 k=1

If the nth partial sum of a series find an S₁ and a₁ an Σa, an n = 1 = = = = n - 3 n + 3 Σ an n = 1 n = 1 (for n = 1) is

2. DETAILS PREVIOUS ANSWERS Which of the following is the power series for arctan(x²) dx ? HINT: The table of series from the first question may be useful here. 22n+4 C + (-1)". (2n + 1)(2n + 4) n=0 00 x4n+3 C +>(-1)". (2n + 1)(4n + 3) C +£ (-1)",2n n=0 in+2 C+>(-1)". (2n + 1) n=0 00 2n+2 C +> (-1)"- (2n + 1)(2n + 2) n=0 gán+1 C+(-1)" (4n +2) 00 (2n + 1) n=0

For what values of x does the series converge conditionally? (-1)+1(x+4) n7" Σ n=1 O A. x= -11 OB. x = 3 OC. x=-11, x = 3 O D. None