Question

2 more questions tonight!

Answer 1

8 + 16 + 24 + . . . + 8n = 4n(n + 1)

Answer 2

let it is true for n=1
so
8(1)=4(1)(1+1)
8=8
fist condition is true
now let
its true for n=k
8 + 16 + 24 + . . . + 8k = 4k(k + 1)
we have to show that it is true for n=k+1

Answer 3

okay how we do that

Answer 4

when n=k+1
we need to show that
8 + 16 + 24 + . . . + 8k +8(K+1)=4(k+1)((k+1)+1)

8 + 16 + 24 + . . . + 8k +8(K+1)= 4k(k + 1)+8(K+1).....1
because
8 + 16 + 24 + . . . + 8k=4k(k+1)
simplify the 1
=4k(k + 1)+8(K+1)
=4k(k+1)+8k+8
=4k^2+4k+8k+8
=4k^2+12k+8
take 4 common

=4(k^2+3k+2)
=4(k+1)((k+2)
or
=4(k+1)((k+1)+1)
Your question i believe is using mathematical induction to prove that that statement is positive for every positive integer n.

Answer 5

im lossst

Answer 6

@wio takeover please. I'm a bit tired D:

Answer 7

@ganeshie8 please help me you usuallyy make me undertsand

Answer 8

That proves your statement btw.