hola. please por favor please help me with my math homework as soon as possible

Question

For a proof by induction of the math statement below, identify the correct step for proving the theorem is true for n = k + 1.

 

 A.)

 

B.)

 

C.)

 

D.)

Answer 1

You assume C and then try to show B

Assume 2+4 + ...2k = k(k+1)

Use that to prove

2+4+ ...2k + 2(k+1) = k(k+1) + 2(k+1)

factor out k+1 on the right side to get

=(k+1)(k+2)

rewrite as

= (k+1)(k+1 + 1)

QED

You reduce the right side to the same form as in the assumption k(k+1) where you replace each k by k+1