hich of the following is a power series representation of the function F(x) O O O O -~(-5) ¹ - (¹) n=0 7 6 n=0 {£¹²¹. n=0 x" [( 5²-(-3) n=0 27 n=0 )^² - (- - - x (65x) (6-4x) -?

True or False

1) Write an equation for determining the nth term of the series 20 + 10 + 5 + 2.5 + ... A) None of these are correct b) t(n) = 1/2n +20 c) t(n) = 1/2 (n−1)+20 d) t(n)=20 . (1/2)^n e) t(n) = 20 ⋅ 1/2^n-1

Evaluate the infinite series by identifying it as the value of a derivative of a geometric series. n(n 1) 5n ∞ n=2 = Hint: Write it as f" 5 where f(x) = ∞ n=0 n x" 25