If Sn denotes the sum of the cubes of the first n natural numbers and sn denotes the sum of the first n natural numbers then find the value of .
Given in the question, Sn denotes the sum of the cubes of the first n natural numbers.
sn denotes the sum of the first n natural numbers.
Note:
I. Sum of first n natural numbers, 1 + 2 +3+…n,
II. Sum of squares of first n natural numbers, 12 + 22 + 32+….n2,
III. Sum of cubes of first n natural numbers, 13 + 23 + 33 +…..n3,
IV. Sum of a constant k, N times,
So,
Sn denotes the sum of the cubes of the first n natural numbers. (Given data in the question).
sn denotes the sum of the first n natural numbers.
To determine the given ratio in the question,
=
So, the value of