Sum of infinity of the series is
Explanation for the correct option :
Step-1 : Assumption and some modification
Let us consider
Dividing both sides of by , we get :
Now, subtracting from , we get :
Step-2 : Finding the value of
Now the R.H.S. of the above equation can be written as .
The series is an infinite geometric series with the first term and common ratio .
We know that the sum of an infinite geometric series with the first term and common ratio is .
So, the sum of will be
Hence,
Step-3 : Finding the value of
We have
Hence, option (D) is the correct answer.