Question

Help ASAP please!!

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

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

Answer 1

2+4+6+...+2k+2(k+1) = k(k+1) + (k+1)(k+1)

Explanation:

Proved case for n

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

for n = k + 1, we replace n by k and add n = k+1 on both sides (

2+4+6+...+2k+2(k+1) = k(k+1) + 2(k+1))

rearrange by factoring the right-hand-side

2+4+6+...+2k+2(k+1) = (k+1)(k+2)

which if we substitute n=k+1, we get back

2+4+6+...+2(n-1) + 2(n) = n(n+1) ...............(2)

This means that equation (1) is applicable to case n+1, and the proof by induction is completed.