Solveeit Logo
Login

Question

Question: \(\sum_{n = 1}^{n}\frac{1}{\log_{3^{n}}a}\)is equal to-...

∑n=1n1log⁡3na\sum_{n = 1}^{n}\frac{1}{\log_{3^{n}}a}is equal to-

A

n(n+1)2\frac{n(n + 1)}{2}log3a

B

n(n+1)2\frac{n(n + 1)}{2}loga3

C

(n+1)24\frac{(n + 1)^{2}}{4}n2log3a

D

None of these

Answer

n(n+1)2\frac{n(n + 1)}{2}loga3

Explanation

Solution

∑n=1n1log⁡3na\sum_{n = 1}^{n}\frac{1}{\log_{3^{n}}a} = loga3 + loga32 + ......+loga3n

=log⁡a3n(n+1)2\log_{a}3^{\frac{n(n + 1)}{2}}= n(n+1)2\frac{n(n + 1)}{2}loga3