Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If n be a positive integer such that  then the value of the sum to n&nbs

If n be a positive integer such that \mathrm{n} \geq 3 then the value of the sum to n terms of the series \\1 . n-\frac{(n-1)}{1 !}(n-1)+\frac{(n-1)(n-2)}{2 !}(n-2)-\frac{(n-1)(n-2)(n-3)}{3 !}(n-3)+\ldots \ldotsis

Option: 1

0


Option: 2

1


Option: 3

-1


Option: 4

none of these


Answers (1)

best_answer

\begin{aligned} & n\left[{ }^{n-1} C_0-{ }^{n-1} C_1 \cdot\left(1-\frac{1}{n}\right)+{ }^{n-1} C_2 \cdot\left(1-\frac{2}{n}\right)-{ }^{n-1} C^3 \cdot\left(1-\frac{3}{n}\right)+\ldots \ldots .\right. \\ & =n[\underbrace{{ }^{n-1} C_0-{ }^{n-1} C_1+{ }^{n-1} C_2-{ }^{n-1} C_3}_{\text {Vanishes }}+\ldots \ldots .]+\left[{ }^{n-1} C_1-2 \cdot{ }^{n-1} C_2+\ldots{ }^{n-1} C_3-4 \cdot{ }^{n-1} C_3+\ldots \ldots\right] \\ & \end{aligned}

For 2^{nd} consider expansion of (1+x)^{n-1} and differentiate w.r.t x and put x = -1

Posted by

Gautam harsolia

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

JEE Main 2026: At IIT Bombay, CSE remains top choice; closing rank falls by 2 points
anam-khan

JEE Main 2026 Registration LIVE: NTA session 1 application soon at jeemain.nta.nic.in; BTech exam dates
anam-khan

JEE Main 2026 Registration LIVE: NTA session 1 applications open soon at jeemain.nta.nic.in; exam dates out

Latest Question