Question

Prove by method of induction, for all n € N.
(1)
2 + 4 + 6 + ..... + 2n=n(n+1)​

Answer 1

Answer:

Step-by-step explanation:

2+4+6+...+2n=2∗(1+2+3+...+n)=2n∗(n+1)2=n∗(n+1)

Second. Suppose that it is true, you have 2+4+6+...+2n=n∗(n+1) This is S(n) add 2(n+1) to both sides, giving

2+4+...+2n+2(n+1)=n∗(n+1)+2(n+1)=(n+2)(n+1)

which is S(n+1)