## Bugay♥ Group Title i need help .. one year ago one year ago

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1. hartnn Group Title

@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♥ Group Title

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♥ Group Title

thanks @hartnn ..

4. DLS Group Title

Satisfy by k Satisfy by k+1

5. hartnn Group Title

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

6. Bugay♥ Group Title

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

7. hartnn Group Title

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♥ Group Title

3 is divisible by 3 then?

9. Bugay♥ Group Title

??

10. Bugay♥ Group Title

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

11. hartnn Group Title

i am sorry, i keep on getting disconnected..

12. Bugay♥ Group Title

oh its ok..

13. hartnn Group Title

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

14. hartnn Group Title

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 Group Title

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

16. Bugay♥ Group Title

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

17. Bugay♥ Group Title

@Tushara : hello..

18. Bugay♥ Group Title

@hartnn : its okey thank you so much..

19. Tushara Group Title

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

20. Bugay♥ Group Title

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

21. Tushara Group Title

22. Tushara Group Title

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

23. Tushara Group Title

the second proof is not true for n=1

24. Bugay♥ Group Title

no..

25. Tushara Group Title

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

26. Bugay♥ Group Title

are you sure??

27. Bugay♥ Group Title

let me check the given..

28. Tushara Group Title

yeah m sure

29. Bugay♥ Group Title

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 Group Title

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

31. Tushara Group Title

its not true for n=2 either

32. Kira_Yamato Group Title

33. Bugay♥ Group Title

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

34. Tushara Group Title

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♥ Group Title

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

36. Tushara Group Title

assume true for n=k

37. Bugay♥ Group Title

@Kira_Yamato : still i thank you..

38. Tushara Group Title

now prove true for n=k+1

39. Bugay♥ Group Title

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

40. Tushara Group Title

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

41. Tushara Group Title

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

42. Bugay♥ Group Title

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

43. Tushara Group Title

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 Group Title

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

45. Bugay♥ Group Title

what should i prove? if it is equal?

46. Tushara Group Title

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

47. Bugay♥ Group Title

oh okey.. thanks..