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anonymous

  • one year ago

help me plz

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    @surjithayer

  3. FireKat97
    • one year ago
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    For 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?

  4. anonymous
    • one year ago
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    UMM OK LOL ?

  5. FireKat97
    • one year ago
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    wait does that make sense? lol

  6. FireKat97
    • one year ago
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    Cus like our teacher was quite strict on following the correct setup and all

  7. anonymous
    • one year ago
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    YES IT DOES BUT I WAS LIKE CHANGING THE OAGE AND SAW ALL THAT I WAS LIKE WTH WHERE DID THAT COME FROM HAHA

  8. anonymous
    • one year ago
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    PAGE

  9. FireKat97
    • one year ago
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    hahaahahhaa

  10. anonymous
    • one year ago
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    ok so go on

  11. FireKat97
    • one year ago
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    okay 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)

  12. anonymous
    • one year ago
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    wait what was step one again haha sorry

  13. FireKat97
    • one year ago
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    hahah no problem, step 1 is to test the condition

  14. FireKat97
    • one year ago
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    so because we are asked to prove for all positive integers, its easiest to test for n =1

  15. anonymous
    • one year ago
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    ok 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

  16. FireKat97
    • one year ago
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    haha 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

  17. anonymous
    • one year ago
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    ok so it would look like umm shiz hah i for got ho to write it haha i jsut ad it sorry

  18. FireKat97
    • one year ago
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    hahah 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

  19. anonymous
    • one year ago
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    omg your so awsome im fanning you haah

  20. FireKat97
    • one year ago
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    hahaha thanks lol I just like helping whenever I can :)

  21. anonymous
    • one year ago
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    ok kool cuz i have like three or four more problems haha

  22. FireKat97
    • one year ago
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    oh I can try and help you with those later, but I gotta after this one, sorry :/

  23. FireKat97
    • one year ago
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    just having a bit of a headache, need rest haha

  24. anonymous
    • one year ago
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    ok kool imm bee done for tonight after this one to maybe idk haha and thnx

  25. FireKat97
    • one year ago
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    hahah okay no problem, yeah its night for you guys, I live in the southern hemisphere so different time zones xD

  26. anonymous
    • one year ago
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    i do to haha i live in south carolina

  27. FireKat97
    • one year ago
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    oh I live in australia so yeah far from US haha

  28. anonymous
    • one year ago
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    well you said southren hemisphere soo i thought the south of the usa opps my bad hah

  29. FireKat97
    • one year ago
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    yeah I wasn't clear lol

  30. anonymous
    • one year ago
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    but ik the times my bff is from newzealand

  31. FireKat97
    • one year ago
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    ohh coool!

  32. anonymous
    • one year ago
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    yeah haha ok so is this problem done or nah haha

  33. FireKat97
    • one year ago
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    okay 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)

  34. FireKat97
    • one year ago
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    do you see what I did there?

  35. anonymous
    • one year ago
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    yeah i got it this time haha

  36. FireKat97
    • one year ago
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    haha 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)

  37. anonymous
    • one year ago
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    yeah

  38. FireKat97
    • one year ago
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    so 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)

  39. FireKat97
    • one year ago
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    does that make sense?

  40. anonymous
    • one year ago
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    yes sir ma'am sir ma'am sir haha

  41. FireKat97
    • one year ago
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    hahaha okay, but we already know that 8 + 16 + 24 + ... + 8k = 4k(k + 1) (from when we let n = k)

  42. anonymous
    • one year ago
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    yeah

  43. FireKat97
    • one year ago
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    so 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

  44. anonymous
    • one year ago
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    yess

  45. FireKat97
    • one year ago
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    and our goal now it to make the LHS look like the RHS

  46. anonymous
    • one year ago
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    omg this is so long haha

  47. FireKat97
    • one year ago
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    hahah ikr thats why they like a formally written proof

  48. FireKat97
    • one year ago
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    so we can make the LHS look like the RHS through factoring out the x + 1

  49. anonymous
    • one year ago
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    this is why this is my last class and im done with school haha

  50. FireKat97
    • one year ago
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    hahahahaha well school isn't that bad

  51. FireKat97
    • one year ago
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    I used to hate it, but you miss it once you leave

  52. FireKat97
    • one year ago
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    well I'm told I should be missing it but meh

  53. anonymous
    • one year ago
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    i will never haha

  54. FireKat97
    • one year ago
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    haha you never know

  55. FireKat97
    • one year ago
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    anyway so once we get the LHS to look like the RHS we can move onto step 3

  56. anonymous
    • one year ago
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    ok i really need to go to my next problem so wnot to be rood but whats next mate ahah

  57. FireKat97
    • one year ago
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    and 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

  58. FireKat97
    • one year ago
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    but yea just make sure you write up the proof with all your steps in a formal way in a test

  59. anonymous
    • one year ago
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    hat should i exactly google

  60. FireKat97
    • one year ago
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    its 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"

  61. FireKat97
    • one year ago
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    and thats your final step

  62. anonymous
    • one year ago
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    thnx on two my next headache haha

  63. FireKat97
    • one year ago
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    haha no problem :) Just post them up and Ill try and take a look a bit later

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