Question

PLEASE HELP Use mathematical induction to prove the statement is true for all positive integers n.

The integer n3 + 2n is divisible by 3 for every positive integer n.

Answer 1

n(n^2 +2)/3

for n=1 ---- 1(1+2)=3/3 =1
n=2 ---- 2(4+2)=12/3=4
n=3 ---- 3(9+2)=33/3=11

for n ---- n(n^2 +2) /3

so using mathinduction we write it for n=k and suppos it true
what will be k(k^2 +2)/3 suppos it true

so than for k=k+1 we get

(k+1)((k+1)^2 +2) /3

for k=1 --- (1+1)((1+1)^2 +2) /3
2(2^2 +2) /3 = 2(4+2) /3 =2*6 /3 = 12/3 =4