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Bugay♥

  • 2 years ago

i need help ..

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  1. hartnn
    • 2 years ago
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    @Bugay♥ Hi :) \(\huge \color{red}{\text{Welcome to Open Study}}\ddot\smile\) Post a specific question, and we'll try our best to help you :)

  2. Bugay♥
    • 2 years ago
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    by the method of mathematical induction prove that the following are valid for all positive values of n. 1.) n^3+2n is divisible by 3 2.) 2+2^2+2^3+ . . . + 2^n = n^2(2n^2-1)

  3. Bugay♥
    • 2 years ago
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    thanks @hartnn ..

  4. DLS
    • 2 years ago
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    Satisfy by k Satisfy by k+1

  5. hartnn
    • 2 years ago
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    welcome :) do you know general steps for proving an identity by mathematical induction ?

  6. Bugay♥
    • 2 years ago
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    basis of induction , induction hypothesis and proof of induction..

  7. hartnn
    • 2 years ago
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    First we prove the result for n= 1 so, put n=1 in n^3+2n and check whether the answer is divisible by 3 .

  8. Bugay♥
    • 2 years ago
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    3 is divisible by 3 then?

  9. Bugay♥
    • 2 years ago
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    ??

  10. Bugay♥
    • 2 years ago
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    hartnn : i thought you will help me.. ???

  11. hartnn
    • 2 years ago
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    i am sorry, i keep on getting disconnected..

  12. Bugay♥
    • 2 years ago
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    oh its ok..

  13. hartnn
    • 2 years ago
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    well, next step is to assume the result true for n=k so, k^3+2k is divisible by 3---->(A)

  14. hartnn
    • 2 years ago
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    now, using (A), we need to prove the result for n=k+1 that is, prove (k+1)^3+2(k+1) is divisible by 3

  15. hartnn
    • 2 years ago
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    using the fact that k^3+2k is divisible by 3 can you do that ? try it...

  16. Bugay♥
    • 2 years ago
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    no i cant :(( can you do it for me?

  17. Bugay♥
    • 2 years ago
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    @Tushara : hello..

  18. Bugay♥
    • 2 years ago
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    @hartnn : its okey thank you so much..

  19. Tushara
    • 2 years ago
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    hey m doing the problem... ill help u out in a bit

  20. Bugay♥
    • 2 years ago
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    @Tushara : i wish you can help me with this..

  21. Tushara
    • 2 years ago
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  22. Tushara
    • 2 years ago
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    does the second proof have any rule on n? like n>1?

  23. Tushara
    • 2 years ago
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    the second proof is not true for n=1

  24. Bugay♥
    • 2 years ago
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    no..

  25. Tushara
    • 2 years ago
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    well then u cant prove the second one.... its just not true

  26. Bugay♥
    • 2 years ago
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    are you sure??

  27. Bugay♥
    • 2 years ago
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    let me check the given..

  28. Tushara
    • 2 years ago
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    yeah m sure

  29. Bugay♥
    • 2 years ago
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    we have to put n=1 to n^2(2n^2-1) right?? and if it is equal to 1 .. the theorem is true for n=1

  30. Tushara
    • 2 years ago
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    2^n=n^2(2n^2-1) for n=1 which is not true

  31. Tushara
    • 2 years ago
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    its not true for n=2 either

  32. Kira_Yamato
    • 2 years ago
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  33. Bugay♥
    • 2 years ago
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    oops im sorry the given was wrong.. it should be 2+2^2+2^3+ . . . + 2^n = 2^(n+1) - 2

  34. Tushara
    • 2 years ago
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    okay,... well its a very easy proof... prove true for n=1, assume true for n=k, then prove true for k+1

  35. Bugay♥
    • 2 years ago
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    it is now true for n=1 right?? then? what i am going to do?

  36. Tushara
    • 2 years ago
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    assume true for n=k

  37. Bugay♥
    • 2 years ago
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    @Kira_Yamato : still i thank you..

  38. Tushara
    • 2 years ago
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    now prove true for n=k+1

  39. Bugay♥
    • 2 years ago
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    then?? i find difficulty in proof of induction :((

  40. Tushara
    • 2 years ago
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    have u practiced any induction problems before? if u have some induction examples in ur math text book... please go thru them

  41. Tushara
    • 2 years ago
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    all u have to do is this: prove that 2^(n+1)-2+2^(n+1)=2(n+2)-2

  42. Bugay♥
    • 2 years ago
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    my teacher dont taught mathematical induction to us.. i havent encounter it before..

  43. Tushara
    • 2 years ago
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    if u cant prove the above equation^ den its best for u to not study ahead and wait for ur teacher to teach u... just see if u can prove the above

  44. Tushara
    • 2 years ago
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    2^(n+1)-2+2^(n+1)=2^(n+2)-2 sorry i typed it up wrong before

  45. Bugay♥
    • 2 years ago
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    what should i prove? if it is equal?

  46. Tushara
    • 2 years ago
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    yes its equal... dats all u have to do for that question

  47. Bugay♥
    • 2 years ago
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    oh okey.. thanks..

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