AP Calculus BC Convergence

Question

Find the sum of the infinite series whose sequence of partial sums, S_n, is  . (4 points)

	10
	0
	9.99
	Sum does not exist

Is the answer A or D? Thank you in advance.

Answer 1

A) 10

n-1

the sum of 1 term = 10-1/2 = 9.5

n=9

sum of 9 terms = 10-1/10 = 9.9

n=999

sum of 999 terms = 10-1/1000 = 9.9999

n=infinity

sum of an infinite number of terms approaches 10

Sn= 10+ 1/infinity = 10+0 = 10