find sum of first six terms in a series

Question

find the sum of first six terms of the series log(2x)+log(4x)+log(8x)+........

 

Answer 1

The series is

Here

So, the series is in Arithmetic progression.

First term , common difference

Formula for term in AP series is  .

term in AP series is

Formula for sum of first n terms is

Sum of first 6 terms is

                                             

                                                           

                                                               

The sum of the first 6 terms is