Question

If the coefficients of 5th and 19th terms in the expansion of (1 + x)n

are equal, then n =​

Answer 1

SOLUTION

GIVEN

The coefficients of 5th and 19th terms in the expansion of $\sf{ {(1 + x)}^{n} }$ are equal

TO DETERMINE

The value of n

EVALUATION

Here the given expansion is $\sf{ {(1 + x)}^{n} }$

So the coefficients of 5th in the expansion

$\sf{ = {}^{n}C_4 }$

So the coefficients of 19th terms in the expansion

$\sf{ = {}^{n}C_{18 }}$

So by the given condition

$\sf{ {}^{n}C_4 = {}^{n}C_{18} }$

$\implies \sf{n = 4 + 18}$

$\implies \sf{n = 22}$

FINAL ANSWER

Hence the required value of n = 22

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. (32C0)^2-(32C1)^2+(32C2)^2-...(32C32)^2=

https://brainly.in/question/28583245

2. (C1/C0) + (2C2 /C1) + ( 3C3/ C2) +.... + nCn/Cn-1= ?

https://brainly.in/question/15423609

Answer 2

$\textbf{Given:}$

$\textsf{The coefficients of 5 th and 19th terms in the expansion of}$

$\mathsf{(1+x)^n\;are\;equal}$

$\textbf{To find:}$

$\textsf{The value of n}$

$\textbf{Solution:}$

$\underline{\textsf{Formula used:}}$

$\mathsf{The\;r\,th\;term\;in\the\;expansion\;of\;(a+b)^n\;is}$

$\boxed{\mathsf{T_{r+1}=n_{C_r}\,a^{n-r}\,b^r}}$

$\mathsf{Consider,\;(1+x)^n}$

$\mathsf{r\,th\,term\;is\;T_{r+1}=n_{C_r}\,x^r}$

$\implies\mathsf{T_5=n_{C_4}\,x^4\;\&\;T_{19}=n_{C_{18}}\,x^{18}}$

$\mathsf{As\;per\;given\;data,}$

$\mathsf{n_{C_4}=n_{C_{18}}}$

$\mathsf{Using}$

$\boxed{\mathsf{If\;n_{C_p}=n_{C_q}\;then\;n=p+q}}$

$\implies\mathsf{n=4+18}$

$\implies\boxed{\mathsf{n=22}}$

$\textbf{Find more:}$