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Bugay♥

i need help ..

  • one year ago
  • one year ago

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  1. hartnn
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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 :)

    • one year ago
  2. Bugay♥
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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)

    • one year ago
  3. Bugay♥
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    thanks @hartnn ..

    • one year ago
  4. DLS
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    Satisfy by k Satisfy by k+1

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

    • one year ago
  6. Bugay♥
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    basis of induction , induction hypothesis and proof of induction..

    • one year ago
  7. hartnn
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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 .

    • one year ago
  8. Bugay♥
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    3 is divisible by 3 then?

    • one year ago
  9. Bugay♥
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    ??

    • one year ago
  10. Bugay♥
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    hartnn : i thought you will help me.. ???

    • one year ago
  11. hartnn
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    i am sorry, i keep on getting disconnected..

    • one year ago
  12. Bugay♥
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    oh its ok..

    • one year ago
  13. hartnn
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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)

    • one year ago
  14. hartnn
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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

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

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

    • one year ago
  17. Bugay♥
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    @Tushara : hello..

    • one year ago
  18. Bugay♥
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    @hartnn : its okey thank you so much..

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

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

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

    • one year ago
  23. Tushara
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    the second proof is not true for n=1

    • one year ago
  24. Bugay♥
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    no..

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

    • one year ago
  26. Bugay♥
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    are you sure??

    • one year ago
  27. Bugay♥
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    let me check the given..

    • one year ago
  28. Tushara
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    yeah m sure

    • one year ago
  29. Bugay♥
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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

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

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

    • one year ago
  32. Kira_Yamato
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    • one year ago
  33. Bugay♥
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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

    • one year ago
  34. Tushara
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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

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

    • one year ago
  36. Tushara
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    assume true for n=k

    • one year ago
  37. Bugay♥
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    @Kira_Yamato : still i thank you..

    • one year ago
  38. Tushara
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    now prove true for n=k+1

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

    • one year ago
  40. Tushara
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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

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

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

    • one year ago
  43. Tushara
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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

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

    • one year ago
  45. Bugay♥
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    what should i prove? if it is equal?

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

    • one year ago
  47. Bugay♥
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    oh okey.. thanks..

    • one year ago
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