A x 1 and x 1 B 1

A. x< -1 and x > 1

B. -1 <= x < 1

C. x< 0

D. x can be any real number

Please explain.

Solution

the series will converge for option B ( -1 <= x < 1 )
because nos. lying between -1 and 1 will be fractions , and fractions raised to power n will give even smaller fraction. for example : 0.5 ^2 = 0.25 which is a smaller n. than 0.5. Since n is a positive no. the series will converge to zero as n tends to infinity.