Which of the following statements is true for the series

Question

Which of the following statements is true for the series  ?

	The series diverges because it is geometric with r =  and a = -1.
	The series converges to 4 because it is geometric with r =  and a = 5.
	The series converges to -1 because it is geometric with r =  and a =  .
	The series diverges because it is geometric with r =  and a = 1.

Answer 1

This is geometric series with a = 1 and r = -1/4. So S_∞ = a/(1 - r) = 1/(1 + 1/4) = 4.

Right answer: converges to 4.