Q24 of 97 Page 199

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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