Mathematics · 2021
JEE Main · 25 July 2021, Shift 1 · Q70
If b is very small as compared to the value of a, so that the cube and other higher powers of b/a can be neglected in the identity 1/(a-b)+1/(a-2…
If $\displaystyle b$ is very small as compared to the value of $\displaystyle a$, so that the cube and other higher powers of $\displaystyle \frac{\mathrm{b}}{\mathrm{a}}$ can be neglected in the identity
$$\frac{1}{a-b}+\frac{1}{a-2 b}+\frac{1}{a-3 b}+\ldots .+\frac{1}{a-n b}=\alpha n+\beta n^2+\gamma n^3,
$$
then the value of $\displaystyle \gamma$ is :
Official answer
(4)
$\displaystyle \frac{b^2}{3 a^3}$
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.