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

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.

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