Home › MCQs › SSC Pure Mathematics › Question #11168
Back to Questions
SSC Pure Mathematics QUESTION #11168
Question 1
Interval of convergence of $\displaystyle\sum_{k=1}^\infty x^k$ is:
  • $]-1,1[$✔️
  • $[-1,1]$
  • $(-\infty,+\infty)$
  • $x=0$
Correct Answer Explanation
The geometric series $\sum_{k=1}^\infty x^k$ converges when $|x| < 1$, i.e. $x\in(-1,1)$. At $x=\pm 1$ the series diverges. The interval of convergence is the open interval $(-1,1) = \,]-1,1[$.