Which statement is true?
a. converges because |a1| < 1 and |r | < 1.
b. converges because |r | < 1 and |a1| does not affect convergence.
c. converges because |a1| > 1 and |r | > 1.
d. converges because |r | > 1 and |a1| does not affect convergence.

Option B is the answer

Step-by-step explanation:

Assuming it is a geometric series

A geometric series will converge if -1< r < 1 written as |r| < 1 .That is if the common ratio is between -1 and 1 like 1/2...For example : 1/2 + 1/4 + 1/8 + ...

if the common ratio, r is greater than 1 or less than -1, the terms of the series become larger and larger in magnitude. The sum of the terms also gets larger and larger, and the series has no sum. The series diverges. For example : 4+ 40+ 400+ 4000 +... The common ration here is 10 and the series diverges. That implies that option C and D are out

For example :

If is r is equal to 1 , that is |r|=1 , all of the terms of the series are the same. For example , 2+2+2+2+... The series diverges.

And the first term doesn't affect the convergence of the series..that implies that option A is out

A series converges if and only if the absolute value of the common ratio is less than one: |r|<1

answer:      

step-by-step explanation: