Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The A.M. of the observations 1.3.5, 3.5.7,  5.7.9, -----,(2 n-1)(2 n+1)(2 n+3) is  Option: 1 <img alt="2 n^3+6 n^2+7 n-

The A.M. of the observations 1.3.5, 3.5.7,  5.7.9, -----,(2 n-1)(2 n+1)(2 n+3) is

 

Option: 1

2 n^3+6 n^2+7 n-2


Option: 2

n^2+8 n^2+7 n-2


Option: 3

2 n^3+5 n^2+6 n-1


Option: 4

2 n^3+8 n^2+7 n-2


Answers (1)

best_answer

A.M. =\frac{1}{n}[1.3 .5+3.5 .7+\ldots+(2 n-1)(2 n+ 1) (2 n+3)]

                    \begin{aligned} & =\frac{1}{n}\left[\sum_{r=1}^n(2 r-1)(2 r+1)(2 r+3)\right] \\ & =\frac{1}{n} \sum_{r=1}^n\left(8 r^3+12 r^2-2 r-3\right) \end{aligned}

=\frac{1}{n}\left[8\left(\frac{n(n+1)}{2}\right)^2+12 \frac{n(n+1)(2 n+1)}{6}-2 \frac{n(n+1)}{2}-3 n\right]

                    \begin{aligned} & =2 n(n+1)^2+2(n+1)(2 n+1)-(n+1)-3 \\ & =2 n^3+8 n^2+7 n-2 . \end{aligned}

Posted by

Pankaj

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

‘Taare Zameen Par’: Bhagwant Mann hails 369 JEE Mains achievers, credits ‘sikhya kranti’ for success
anam-khan

JEE Mains 2026 LIVE: JEE Advanced registration closes on May 2; exam date and timing, BTech cutoffs
anam-khan

JEE Main 2026 toppers reveal success mantras; practice, precision, and perfect strategy

Latest Question