(-1)" ( b) Σ 2n Test: diverges converges n=0 Reason: (e) * (1+ 4)" Test: diverges converges n=1 Reason:

Evaluate the infinite series by identifying it as the value of an integral of a geometric series. (- 1)" 57+ (n + 1) 8. n+1 1 | f(t)dt where f(x) = (– 1)" Hint: Write it as 5 + I n=0

∞ Suppose ak > 0 for all k, and ∑ ak converges.                                                   k=1 Answer the following questions and explain your reasoning.               ∞        a. Must ∑−3an always converge?               n=1               ∞b. Must ∑ 1/an always converge?              n=1              ∞ c. Must ∑(an )^3 always converge?              n=1             ∞ d. Must ∑ (an)^1/3 always converge?               n=1

ENERGEL Needle Tip 0.5 mm ball Give an example of two divergent sequences {x} and {y} = such that... C a.) { xn³. - {yn=1 converges where b.) Exn ynn, converges where Xn xn #yn Xn #yn \nEN Xn # / VEN Yn