Question

Using principle of mathematical induction prove that : n3

-7n+3 is divisible

by 3 for all n∈N.​

Answer 1

Step-by-step explanation:

HEY MATE ..

ANSWER

ANSWERf(n)=n 3 +2n

ANSWERf(n)=n 3 +2nput n=1, to obtain f(1)=1 /3+2.1=3

3+2.1=3Therefore, f(1) is divisible by 3Assume that for n=k, f(k)=k 3 +2k is divisible by 3Now, f(k+1)=(k+1) 3 +2(k+1)=k 3 +2k+3(k 2 +k+1)=f(k)+3(k 2 +k+1)Since, f(k) is divisible by 3Therefore, f(k+1) is divisible by 3and from the principle of mathematical induction f(n) is divisible by 3 for all n∈N