Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find the sum of the first n terms of the series: 3+ 7 +13 +21 +31 +…

23.   Find the sum of the first n terms of the series: 3+ 7 +13 +21 +31 +…

Answers (1)

best_answer

The series: 3+ 7 +13 +21 +31 +…..............

n th term  = n^2+n+1=a_n

S_n=\sum _{k=1}^{n} a_k=\sum _{k=1}^{n} k^{2}+k+1

                        =\sum _{k=1}^{n} k^2+\sum _{k=1}^{n} k+\sum _{k=1}^{n} 1

                     =\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}+n

                   =n\left ( \frac{(n+1)(2n+1)}{6}+\frac{n+1}{2}+1 \right )

                   =n\left ( \frac{(n+1)(2n+1)+3(n+1)+6}{6} \right )

                  =n\left ( \frac{2n^2+n+2n+1+3n+3+6}{6} \right )

                  =n\left ( \frac{2n^2+6n+10}{6} \right )

                   =n\left ( \frac{n^2+3n+5}{3} \right )

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question