If S 1 , S 2 , S 3 are the sum of first n natural numbers, their squares and their cubes, respectively, show that

Question

Philoid · Accepted Answer

According to question -

S₁ = 1 + 2 + 3 + … + n =

S₂ = 1² + 2² + 3² + … + n² =

S₃ = 1³ + 2³ + 3³ + … + n³ =

Now,

R.H.S = S₃(1 + 8S₁)

= R.H.S

Hence, L.H.S = R.H.S

Hence Proved.

If S1, S2, S3 are the sum of first n natural numbers, their squares and their cubes, respectively, show that