The sum of the infinite terms of the following series will be
Explanation for the correct option:
Let the sum be
Subtracting from ,
We can see that the terms in the bracket in excluding the is in geometric progression.
The sum of a geometric series (geometric series is a sum whose terms are in geometric progression) with infinite terms and common ratio less than is given as,
where is the first term and is the common ratio.
Here, and
Thus, How? Explain the formula used
Therefore, the sum of the infinite series is .
Hence, the correct option is (D).