Question

Use mathematical induction to prove that the statement is true for every positive integer n.
8 + 16 + 24 + . . . + 8n = 4n(n + 1)

Answer 1

@bibby

Answer 2

there are two parts to induction proof
basis case and inductive step

Answer 3

How do I solve this then?

Answer 4

or like how do I answer this ?

Answer 5

assume the base case is true and prove it for k+1

Answer 6

lets not skip the 'basis' case , (i mean)

Answer 7

is this statement true for n=1 ?

Answer 8

what does that entail? prove it for n=1 or 2 and then prove it holds true for n+1?

Answer 9

firstly put n=1 .and find out if its true or not

Answer 10

prove it for n=1 ,
then prove that if true for k , then its true for k+1

Answer 11

separately

Answer 12

I see. my bad

Answer 13

guys, finish your helps, please.

Answer 14

it might be easier if we rewrite the expression using P(n)

Answer 15

@perl go to my post to help me, I can handle here

Answer 16

check that
8*1 = 4(1)(1+1)

Answer 17

the series is the sum of n multiples of 8
so n=1: 8
n=2: 8+16
etc.
prove that 8=(1)(4)(1+1)

Answer 18

basis step: past
hypothesis step: assume it is true for k , that is
8+16+.....+8k = 4k(k+1)
now, need prove it is true for k+1, that is

Answer 19

8+16+......+8k + 8(k+1)= 4(k+1)(k+1+1)=4(k+1)(k+2)

Answer 20

hint: add 8(k+1) to both sides of that equation

Answer 21

loser66, be careful about your right side of equation (that is what we want to prove)

Answer 22

oh, I think you are at my post @perl

Answer 23

I know, I just let it there to know what we have to get from the left hand side.