Question

Assertion :The $n^{th}$ term of the series $1+\frac{2}{3}+\frac{3}{3^2}+\frac{4}{3^3}+...\infty is\frac{n}{3^{n-1}}$ Reason: The $n^{th}$ term of an of an $A.G.P$ is the product of $n^{th}$ terms of corresponding $A.P.$ & $G.P.$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$t_n$ of AGP $=\frac{n}{3^{n-1}}$
Hence, Assertion is correct
$t_n$ of AP $=n$
GP is $1,\frac{1}{3},\frac{1}{3^2},...$
$T_n$ of GP $=\frac{1}{3^{n-1}}$
$t_n.T_n=\frac{n}{3^{n-1}}$
Hence, A is correct