Find the values of x for which the series converges.

Question

Find the values of x for which the series  converges.

Quizplus · Accepted Answer

This question is related to the hexadecimal representation of a number. The given series can be written as:
$11+\frac{14a+c}{16}+\frac{4f}{16^2}+\frac{ec3a}{16^3}+\frac{fae7bedf}{16^4}+\frac{3bb74a025b23}{16^5}+TB7497+11$
For this series to converge, each term of the series should tend to zero as the index tends to infinity. Since the 5th term of the series is the largest, we need to focus on it.
$\frac{3bb74a025b23}{16^5}=\frac{649483685887491}{1048576}$
Since this term is a constant, for the series to converge, this constant term needs to be zero. To make it zero, we need to change the 12th digit from the right, which is currently a '3', to a 'b'. That only happens in option D. Hence, D is the correct choice.

Find the Values of X for Which the Series