Q24 of 36 Page 161

Let Sn denote the sum of the cubes of the first n natural numbers and sn denote the sum of the first n natural numbers. Then equals.

Given that:

Sn = sum of the cubes of first n natural numbers


sn = Sum of the first n natural numbers


&


Let Tn be the nth term of the above series


…(i)


We know that,


Sum of cubes of first n natural numbers



and sum of first n natural numbers



∴, eq. (i) becomes





Now, sum of the given series










Hence, the correct option is (a)

More from this chapter

All 36 →
22

Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n : Sn is equal to

 23

The minimum value of 4x + 41–x, x ∈ R, is

 25

If tn denotes the nth term of the series 2 + 3 + 6 + 11 + 18 + ... then t50 is

 26

The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm3 and the total surface area is 252 cm2. The length of the longest edge is