First slide

Binomial theorem for positive integral Index

Question

If $(1 + a x)^{n} = 1 + 10 x + 40 x^{2} + \dots . .,$ then value of $\frac{a + n}{a - n}$ is

Moderate

A

5/7
B

7/3
C

–5/7
D

– 7/3

Solution

$n a = 10, 40 = \frac{n (n - 1)}{2} a^{2}$
$\frac{80}{100} = \frac{n (n - 1) a^{2}}{n^{2} a^{2}} \Rightarrow \frac{4}{5} = \frac{n - 1}{n} \Rightarrow n = 5$
and $a = 2$

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