Question

Check my answer: Use mathematical induction to prove the statement is true for all positive integers n.
8 + 16 + 24 + ... + 8n = 4n(n + 1)

Answer 1

8+16+24+...+8k=4k(k+1)
When we start off with k, we get 8k. Sk would equal 4k(k+1)
When we use the next integer, k+1, we get 8(k+1). S(k+1) would equal 8k+8(k+1)=8k+8k+8=16k+8=8(2k+1)

Answer 2

Then I'm stuck there.

Answer 3

@Mertsj

Answer 4

let p(n)=8+16+24+....+8n=4n(n+1)
for n=1,p(1)=4*1(1+1)=4*2=8
hence p(1) is true.
assume that p(k) is true.
8+16+24+...+8k=4k(k+1)
adding both sides 8(k+1),we get
8+16+24+...+8k+8(k+1)=4k(k+1)+8(k+1)=4(k+1)(k+2)=p(k+1)(k+1+1)=p(k+1)
therefore if p(k) is true then p(k+1) is also true.
Hence by induction p(n) is true for all positive integers.