What is the sum of the series $1 + (1 + x) + (1 + x + x^2) + (1 + x + x^2 + x^3) + \dots$ up to $n$ terms?

  • A
    $\frac{1 - x^n}{1 - x}$
  • B
    $\frac{x(1 - x^n)}{1 - x}$
  • C
    $\frac{n(1 - x) - x(1 - x^n)}{(1 - x)^2}$
  • D
    None of these

Explore More

Similar Questions

What is the sum of the first $10$ terms of the series $0.7 + 0.77 + 0.777 + \dots$?

The sequence of natural numbers is divided into groups as follows: $(1), (2, 3), (4, 5, 6), (7, 8, 9, 10), \dots$. Find the sum of the numbers in the $n^{th}$ group.

Difficult
View Solution

If $S_n = 1^3 + 2^3 + \ldots + n^3$ and $T_n = 1 + 2 + \ldots + n$,then

The sum to $n$ terms of the series $2^2 + 4^2 + 6^2 + \dots$ is

If the sum of the squares of the first $n$ natural numbers exceeds their sum by $330$,then $n = $

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo