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hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0@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 :)

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0by 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^21)

DLS
 2 years ago
Best ResponseYou've already chosen the best response.0Satisfy by k Satisfy by k+1

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0welcome :) do you know general steps for proving an identity by mathematical induction ?

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0basis of induction , induction hypothesis and proof of induction..

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0First we prove the result for n= 1 so, put n=1 in n^3+2n and check whether the answer is divisible by 3 .

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.03 is divisible by 3 then?

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0hartnn : i thought you will help me.. ???

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0i am sorry, i keep on getting disconnected..

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0well, next step is to assume the result true for n=k so, k^3+2k is divisible by 3>(A)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0now, 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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0using the fact that k^3+2k is divisible by 3 can you do that ? try it...

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0no i cant :(( can you do it for me?

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0@hartnn : its okey thank you so much..

Tushara
 2 years ago
Best ResponseYou've already chosen the best response.1hey m doing the problem... ill help u out in a bit

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0@Tushara : i wish you can help me with this..

Tushara
 2 years ago
Best ResponseYou've already chosen the best response.1does the second proof have any rule on n? like n>1?

Tushara
 2 years ago
Best ResponseYou've already chosen the best response.1the second proof is not true for n=1

Tushara
 2 years ago
Best ResponseYou've already chosen the best response.1well then u cant prove the second one.... its just not true

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0let me check the given..

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0we have to put n=1 to n^2(2n^21) right?? and if it is equal to 1 .. the theorem is true for n=1

Tushara
 2 years ago
Best ResponseYou've already chosen the best response.12^n=n^2(2n^21) for n=1 which is not true

Tushara
 2 years ago
Best ResponseYou've already chosen the best response.1its not true for n=2 either

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0oops im sorry the given was wrong.. it should be 2+2^2+2^3+ . . . + 2^n = 2^(n+1)  2

Tushara
 2 years ago
Best ResponseYou've already chosen the best response.1okay,... well its a very easy proof... prove true for n=1, assume true for n=k, then prove true for k+1

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0it is now true for n=1 right?? then? what i am going to do?

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0@Kira_Yamato : still i thank you..

Tushara
 2 years ago
Best ResponseYou've already chosen the best response.1now prove true for n=k+1

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0then?? i find difficulty in proof of induction :((

Tushara
 2 years ago
Best ResponseYou've already chosen the best response.1have u practiced any induction problems before? if u have some induction examples in ur math text book... please go thru them

Tushara
 2 years ago
Best ResponseYou've already chosen the best response.1all u have to do is this: prove that 2^(n+1)2+2^(n+1)=2(n+2)2

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0my teacher dont taught mathematical induction to us.. i havent encounter it before..

Tushara
 2 years ago
Best ResponseYou've already chosen the best response.1if 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

Tushara
 2 years ago
Best ResponseYou've already chosen the best response.12^(n+1)2+2^(n+1)=2^(n+2)2 sorry i typed it up wrong before

Bugay♥
 2 years ago
Best ResponseYou've already chosen the best response.0what should i prove? if it is equal?

Tushara
 2 years ago
Best ResponseYou've already chosen the best response.1yes its equal... dats all u have to do for that question
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