Question

What am I missing from my answers below this question?
Use mathematical induction to prove the statement is true for every positive integer n.
8+16+24+...+8n=4n(n+1)
ANSWER: 8n=4n(n+1)
8(1)=4(1)(1+1)
8=8 (Proved correct)

ANSWER: 4k(k+1)=8
4(1) (1+1) = 8
4 (2) = 8
8 = 8 (Proved correct.

Answer 1

Mathematical induction requires you to check if P(0) is true
then You assume P(n) is true, you have to show that if P(n) is true then
P(n+1) is also true
therefore your statement as is true

Answer 2

So my answer then is correct.

Answer 3

well not really! you have proven that for n=1 your statement is valid
but where is the assumption that P(n) is true
then prove that p(n+1) is true?

Answer 4

when you do P(n) and P(n+1) you don't check for specific examples
you need to prove for general case

Answer 5

Oh geez. Help then please?\

Answer 6

Okay! Assume P(n) is true
that is saying that 8+16+24+....+8n=4n(n+1) is true

Answer 7

now we check that if P(n+1) is true or not
so P(n+1): 8+16+24+....+8(n+1)=4(n+1)(n+2)

Answer 8

So far good , yes?

Answer 9

Hold on one moment, so I can review what you have shown me.

Answer 10

eh i have to go to class so be quick hehhe

Answer 11

we added (n+2) to the equation

Answer 12

No we just plug in n+1 in place of n so we can get n+1 expression
and we need to show that indeed is equal and true
in P(n+1) i put = sign but we are still asking is this true? you got me
the point is to show that left hand side is indeed equal right hand side

Answer 13

we going to use our assumption that P(n) is true that we assumed!

Answer 14

Got it. And that I believe would be the only equation I am missing . I knew it. Thanks.

Answer 15

okay! Actually you missed to the assumption too
cause if you didn't do this step you are not going to solve this

Answer 16

And you are welcome^_^

Answer 17

I got it. Thanks and have a good class.

Answer 18

Welcome mate! good luck with this
to better get the hang of it practice more example with different settings

Answer 19

Am doing that, but after a few hours the brain freezes and you begin doubting work you've done. Have to learn to take breaks in between! Thanks again.