Q. 244.0( 21 Votes )

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

Answer :

According to question -

S_{1} = 1 + 2 + 3 + … + n =

S_{2} = 1^{2} + 2^{2} + 3^{2} + … + n^{2} =

S_{3} = 1^{3} + 2^{3} + 3^{3} + … + n^{3} =

Now,

R.H.S = S_{3}(1 + 8S_{1})

*=* R.H.S

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

Hence Proved.

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