Sum of the first terms of the following series is
Explanation for the correct option :
Step 1 : Reforming the given series
Let be the sum of the first terms of the given series i.e. . We can write as
Step 2 : Calculating the above summations
Formula to be used : We know that the sum of the first natural numbers is , the sum of the squares of the first natural numbers is and the sum of the cubes of the first natural numbers is .
So,
Also,
Step 3 : Finding the value of
From Step-1, using the values obtained in Step-2, we can get the value of as follows :
Hence, option (A) is the correct answer.