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anonymous
 one year ago
Mathematical induction
anonymous
 one year ago
Mathematical induction

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can someone help me with this? Don't just give me the answer but i need the steps too cuz i don't understand it. Thanks :)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1well we should start with the first step ... is it true for some value of n? are we restricted by our n values? these usually define a domain

freckles
 one year ago
Best ResponseYou've already chosen the best response.1that one line seems to be missing +2(k+1)+6 on the left hand side

freckles
 one year ago
Best ResponseYou've already chosen the best response.1it is also missing a square on the (k+1)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1lol, your giving out answers

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1what is the question? is it asking if the setup is correct?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I thought it was asking to use this to prove this

freckles
 one year ago
Best ResponseYou've already chosen the best response.1lol I didn't know I was giving answers

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yep it is asking if it is correct

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1then we would walk thru the process, to determine if the step they propose is valid.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1as freckles pointed out already ... its missing alot of stuff tho

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I guess it kind of does make sense as a true false question.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1hint: \[\text{ If give } P_n \text{ to find } P_{k+1} \text {just replace the } n \text{ 's with } (k+1)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1on both left and right hand sides of the equation

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1id say that replacement depends on the structure of the problem

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1the proofing in this case requires us to add the (k+1)th term to each side and see if it simplifies to a format that looks as if all we did was replace n by (k+1)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh wait so since when you substitute the n's for (k+1) the top equation has a k^2 and the bottom doesn't so it already wouldn't be equal?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1right but there is also another thing missing on the left hand side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would the left side turn into 2k+8 or something?

freckles
 one year ago
Best ResponseYou've already chosen the best response.12(k+1)+6 2k+2+6 2k+8 yep that should be the last term on the left hand side where the one before it was 2k+6

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you know because if it was 8+10+12+...+(2k+6) which is the exact thing as 8+10+12+...+(2n+6) except we have k instead of n then we should have this is k^2+7k since that other one is n^2+7n

freckles
 one year ago
Best ResponseYou've already chosen the best response.1And sorry about taking the fun out of the problem... I didn't realize the question was is this true or not at first.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I thought we were going to prove something. :( And there was just a lot of typeo.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Its okay haha at least i understand it now. Thank you :)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and yeah the way we prove it is true for k+1 is take that previous thing replace n's with k's then as @amistre64 said had the (k+1)th term on both sides which you already know is +(2k+8) \[\color{red}{8+10+12+\cdots+(2k+6)}+(2k+8)=\color{red}{k^2+7k}+(2k+8) \\ \text{ where we want to show the right hand side actually does equal } \\ (k+1)^2+7(k+1)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and if you are doing that you might have an easier time expanding (k+1)^2+7(k+1) to show it is the same as k^2+7k+(2k+8)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1but anyways this is getting into the actual proof of the P_n thing is true for all positive integer n
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