Prove the following by the principle of mathematical induction:`(n^(11))/(11)+(n^5)/5+(n^3)/3+(62)/(165)n` is a positive integer for `n in NNdot`

Explanation

Let `P(n)` be the given statement.

Now.

`P(n): frac{n^{11}}{11}+frac{n^{5}}{5}+frac{n^{3}}{3}+frac{62}{165} n` is a positive integer for all `n in N`.

Step 1 :

`P(1)=frac{1}{11}+frac{1}{5}+frac{1}{3}+frac{62}{165}=frac{15+33+55+62}{165}=frac{165}{165}=1`

It is certainly a positive integer.

Hence, `P(1)` is true .

step2:

...