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anonymous
 one year ago
help me plz
anonymous
 one year ago
help me plz

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FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1For mathematical induction proofs, it is very important to follow through each step carefully, and our first step should be to test the condition. so we are asked to prove for all positive integers, so can you write out the test for a positive integer for step 1?

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1wait does that make sense? lol

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1Cus like our teacher was quite strict on following the correct setup and all

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0YES IT DOES BUT I WAS LIKE CHANGING THE OAGE AND SAW ALL THAT I WAS LIKE WTH WHERE DID THAT COME FROM HAHA

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1okay so after you test for your first step, you want to let n = k for your second step (another useless convention I suppose but it was necessary for us) so its like... Step 2, for n = k 8 + 16 + 24 + ... + 8k = 4k(k + 1)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait what was step one again haha sorry

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1hahah no problem, step 1 is to test the condition

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1so because we are asked to prove for all positive integers, its easiest to test for n =1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok how do i do that agin hah im sorry i was at base untill 8pm cuz my comander is an retriceso im very sleepy and slow haha

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1haha no problem, so you can test this by saying; test for n = 1 and then sub n = 1 into both the left and right hand sides and show that they are equal

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so it would look like umm shiz hah i for got ho to write it haha i jsut ad it sorry

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1hahah don't worry, so you just sub n = 1 into left and right hand side so LHS = 8(1) = 8 RHS = 4(1)(1 + 1) = 4(2) = 8 therefore LHS = RHS and the test is true for n = 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0omg your so awsome im fanning you haah

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1hahaha thanks lol I just like helping whenever I can :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok kool cuz i have like three or four more problems haha

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1oh I can try and help you with those later, but I gotta after this one, sorry :/

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1just having a bit of a headache, need rest haha

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok kool imm bee done for tonight after this one to maybe idk haha and thnx

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1hahah okay no problem, yeah its night for you guys, I live in the southern hemisphere so different time zones xD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i do to haha i live in south carolina

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1oh I live in australia so yeah far from US haha

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well you said southren hemisphere soo i thought the south of the usa opps my bad hah

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1yeah I wasn't clear lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but ik the times my bff is from newzealand

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah haha ok so is this problem done or nah haha

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1okay so lets continue with the question so for step 2 we start off by letting n = k to get 8 + 16 + 24 + ... + 8k = 4k(k + 1) then we want to let n = k + 1 and do a similar thing, subbing in K + 1 for all 'n's so we get Let n = k + 1 8 + 16 + 24 + ... + 8(k + 1) = 4(k + 1)(k + 1 + 1)

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1do you see what I did there?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah i got it this time haha

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1haha okay cool so now do you notice how we can rewrite the above line as 8(1) + 8(2) + 8(3) + ... +8(k + 1) = 4(k + 1)(k + 2)

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1so following that trend, we can write 8(k) before the 8(k + 1) so we get 8 + 16 + 24 + ... + 8k + 8(k+1) = 4(k + 1)(k + 2)

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1does that make sense?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes sir ma'am sir ma'am sir haha

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1hahaha okay, but we already know that 8 + 16 + 24 + ... + 8k = 4k(k + 1) (from when we let n = k)

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1so we can substitute that in, so rather than having 8 + 16 + 24 + ... + 8k + 8(k + 1) = 4(k + 1)(k + 2) we can now have 4k(k + 1) + 8(k + 1) = 4(k + 1)(k + 2) instead

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1and our goal now it to make the LHS look like the RHS

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0omg this is so long haha

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1hahah ikr thats why they like a formally written proof

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1so we can make the LHS look like the RHS through factoring out the x + 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this is why this is my last class and im done with school haha

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1hahahahaha well school isn't that bad

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1I used to hate it, but you miss it once you leave

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1well I'm told I should be missing it but meh

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1anyway so once we get the LHS to look like the RHS we can move onto step 3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok i really need to go to my next problem so wnot to be rood but whats next mate ahah

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1and for step 3, we just need to kind of sum stuff up and say that by the law of mathematical induction.. blah blah blah (Im pretty sure you can google one of these statements, i don't remember them exactly) we have proven that the above statement is true for all positive integers

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1but yea just make sure you write up the proof with all your steps in a formal way in a test

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hat should i exactly google

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1its actually just something along the lines of "According to the Principle of Mathematical Induction P(n) is true for any positive integer, as proven above"

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1and thats your final step

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thnx on two my next headache haha

FireKat97
 one year ago
Best ResponseYou've already chosen the best response.1haha no problem :) Just post them up and Ill try and take a look a bit later
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