(2) Determine whether the following series converge. Rigorously justify your answers (using the convergence tests from the lecture). ∞ ∞ (a) Σ n 2n (b) n2+1 n! n=1 n=1 ∞ շո (c) Σ 1+2n n=0 (α) Σ ΣΣΣ (e) (-1)+1 +1 n=1 n=1 n! 1 (f) 3n+2' n=1 (2n)!*

#4 Need a,b,c,d, e and f

1. ( ) Find the Interval of Convergence for the following Power Series. (-1)+¹(x - 2)" n2" ∞ n=1

5. Determine if the following series converge conditionally, converge absolutely, or diverge. Justify your steps and cite the appropriate theorems and convergence/divergence tests. n=1 (-1)"√√n³-1 4n-1 3+ b) Σ(³+n)" 5n n=1 c) Σ cOS (1/3) (-1)-1 α)Ÿ= 5n²-4n+3 n=1 n=1 4" 3n+7n