Prove by induction that the sum `S_n=n^3+2n^2+5n+3` is divisible by `3` for all `n in Ndot`

Explanation

`P(n):n^3+3n^2+5n+3 ` is divisible by 3

`∴P(1):1^3+3×1^2+5×1+3
=1+3+5+3=12` which is divisible by 3

∴P(1) is true

Let `P(m):m^3+3m^2+5m+3` is divisible by 3 is true

Then, we have to prove that p(m+1) is also true

`P(m+1):(m+1)^3+3(m+1)^2+5(m+1)+3`

`=m^3+1+3m(m+1)+3(m^2+1+2m)+5m+5+3`

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