Step 1 We will use the Ratio Test to determine the radius of convergence. We have the following. th+ 7 an + 1 8(n + 1)! lim lim an xh + 6 8n! th +7 8 n! lim п! %D n → o 8(n + 1)! th + 6 Step 2 Simplifying, we get lim n → 00

Use the formula for the sum of the first ii terms of an arithmetic series to find the sum of the first eleven terms of the arithmetic series 2.5,4,5.5,

Prove the formula for the sum of the first n terms of an arithmetic series: a+a+d+a+2d+a+n-1d=na+an2 where an=a+n-1d.

A ball has a bounce-back ratio 35 . of the height of the previous bounce. Write a series representing the total distance traveled by the ball, assuming it was initially dropped from a height of 5 feet. What is the total distance? (Hint: the total distance the ball travels on each bounce is the sum of the heights of the rise and the fall.)

What is a geometric series?

Find the sum of the first five terms of the sequence with the given general term. an=n