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hartnn Group TitleBest 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 :)
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
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^21)
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
thanks @hartnn ..
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.0
Satisfy by k Satisfy by k+1
 one year ago

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

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
basis of induction , induction hypothesis and proof of induction..
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.0
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

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
3 is divisible by 3 then?
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
hartnn : i thought you will help me.. ???
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.0
i am sorry, i keep on getting disconnected..
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
oh its ok..
 one year ago

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

hartnn Group TitleBest ResponseYou've already chosen the best response.0
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

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

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
no i cant :(( can you do it for me?
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
@Tushara : hello..
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
@hartnn : its okey thank you so much..
 one year ago

Tushara Group TitleBest ResponseYou've already chosen the best response.1
hey m doing the problem... ill help u out in a bit
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
@Tushara : i wish you can help me with this..
 one year ago

Tushara Group TitleBest ResponseYou've already chosen the best response.1
does the second proof have any rule on n? like n>1?
 one year ago

Tushara Group TitleBest ResponseYou've already chosen the best response.1
the second proof is not true for n=1
 one year ago

Tushara Group TitleBest ResponseYou've already chosen the best response.1
well then u cant prove the second one.... its just not true
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
are you sure??
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
let me check the given..
 one year ago

Tushara Group TitleBest ResponseYou've already chosen the best response.1
yeah m sure
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
we 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
 one year ago

Tushara Group TitleBest ResponseYou've already chosen the best response.1
2^n=n^2(2n^21) for n=1 which is not true
 one year ago

Tushara Group TitleBest ResponseYou've already chosen the best response.1
its not true for n=2 either
 one year ago

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

Tushara Group TitleBest ResponseYou've already chosen the best response.1
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

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

Tushara Group TitleBest ResponseYou've already chosen the best response.1
assume true for n=k
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
@Kira_Yamato : still i thank you..
 one year ago

Tushara Group TitleBest ResponseYou've already chosen the best response.1
now prove true for n=k+1
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
then?? i find difficulty in proof of induction :((
 one year ago

Tushara Group TitleBest ResponseYou've already chosen the best response.1
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

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

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
my teacher dont taught mathematical induction to us.. i havent encounter it before..
 one year ago

Tushara Group TitleBest ResponseYou've already chosen the best response.1
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

Tushara Group TitleBest ResponseYou've already chosen the best response.1
2^(n+1)2+2^(n+1)=2^(n+2)2 sorry i typed it up wrong before
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
what should i prove? if it is equal?
 one year ago

Tushara Group TitleBest ResponseYou've already chosen the best response.1
yes its equal... dats all u have to do for that question
 one year ago

Bugay♥ Group TitleBest ResponseYou've already chosen the best response.0
oh okey.. thanks..
 one year ago
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