## Bugay♥ 2 years ago i need help ..

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1. hartnn

@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♥

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♥

thanks @hartnn ..

4. DLS

Satisfy by k Satisfy by k+1

5. hartnn

welcome :) do you know general steps for proving an identity by mathematical induction ?

6. Bugay♥

basis of induction , induction hypothesis and proof of induction..

7. hartnn

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♥

3 is divisible by 3 then?

9. Bugay♥

??

10. Bugay♥

hartnn : i thought you will help me.. ???

11. hartnn

i am sorry, i keep on getting disconnected..

12. Bugay♥

oh its ok..

13. hartnn

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

14. hartnn

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

using the fact that k^3+2k is divisible by 3 can you do that ? try it...

16. Bugay♥

no i cant :(( can you do it for me?

17. Bugay♥

@Tushara : hello..

18. Bugay♥

@hartnn : its okey thank you so much..

19. Tushara

hey m doing the problem... ill help u out in a bit

20. Bugay♥

@Tushara : i wish you can help me with this..

21. Tushara

22. Tushara

does the second proof have any rule on n? like n>1?

23. Tushara

the second proof is not true for n=1

24. Bugay♥

no..

25. Tushara

well then u cant prove the second one.... its just not true

26. Bugay♥

are you sure??

27. Bugay♥

let me check the given..

28. Tushara

yeah m sure

29. Bugay♥

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^n=n^2(2n^2-1) for n=1 which is not true

31. Tushara

its not true for n=2 either

32. Kira_Yamato

33. Bugay♥

oops im sorry the given was wrong.. it should be 2+2^2+2^3+ . . . + 2^n = 2^(n+1) - 2

34. Tushara

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♥

it is now true for n=1 right?? then? what i am going to do?

36. Tushara

assume true for n=k

37. Bugay♥

@Kira_Yamato : still i thank you..

38. Tushara

now prove true for n=k+1

39. Bugay♥

then?? i find difficulty in proof of induction :((

40. Tushara

have u practiced any induction problems before? if u have some induction examples in ur math text book... please go thru them

41. Tushara

all u have to do is this: prove that 2^(n+1)-2+2^(n+1)=2(n+2)-2

42. Bugay♥

my teacher dont taught mathematical induction to us.. i havent encounter it before..

43. Tushara

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^(n+1)-2+2^(n+1)=2^(n+2)-2 sorry i typed it up wrong before

45. Bugay♥

what should i prove? if it is equal?

46. Tushara

yes its equal... dats all u have to do for that question

47. Bugay♥

oh okey.. thanks..