If the sum of the first ten terms of the series $\frac{1}{5}+\frac{2}{65}+\frac{3}{325}+\frac{4}{1025}+\frac{5}{2501}+\ldots$ is $\frac{m}{n}$, where m and n are co-prime numbers, then $m+n$ is equal to ____________.

JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 June 2022, Shift 1, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

If the sum of the first ten terms of the series

\frac{1}{5}+\frac{2}{65}+\frac{3}{325}+\frac{4}{1025}+\frac{5}{2501}+\ldots

\frac{m}{n}

, where m and n are co-prime numbers, then

m+n

is equal to ____________.

Official answer

276

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: Method of Differences (Vn Method)

Same idea in other shifts

Asked 7× in all

5 Apr 2026, Shift 2 · Q5If the sum of the first 10 terms of the series…HardSingle correct
2 Apr 2025, Shift 2 · Q22If the sum of the first 10 terms of the series…HardNumerical value
9 Apr 2024, Shift 1 · Q5If the sum of the series $\frac{1}{1\cdot(1+d)}+\frac{1}{(1+d)(1+2d)}+\ldots+\frac{1}{(1+9d)(1+10d)}$ is equal to $5$ , then $50d$ is equal…MediumSingle correct
6 Apr 2023, Shift 1 · Q8Let $a_1,a_2,a_3,\ldots,a_n$ be $n$ positive consecutive terms of an arithmetic progression. If $d>0$ is its common difference, then…MediumSingle correct
29 Jul 2022, Shift 1 · Q28If…MediumNumerical value
30 Jun 2022, Shift 1 · Q7The value of $1 + \frac{1}{1+2} + \frac{1}{1+2+3} + \ldots + \frac{1}{1+2+3+\ldots+11}$ is equal to :EasySingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.