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Mathematics
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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 :)
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)
thanks @hartnn ..

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Other answers:

  • DLS
Satisfy by k Satisfy by k+1
welcome :) do you know general steps for proving an identity by mathematical induction ?
basis of induction , induction hypothesis and proof of induction..
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 .
3 is divisible by 3 then?
??
hartnn : i thought you will help me.. ???
i am sorry, i keep on getting disconnected..
oh its ok..
well, next step is to assume the result true for n=k so, k^3+2k is divisible by 3---->(A)
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
using the fact that k^3+2k is divisible by 3 can you do that ? try it...
no i cant :(( can you do it for me?
@Tushara : hello..
@hartnn : its okey thank you so much..
hey m doing the problem... ill help u out in a bit
@Tushara : i wish you can help me with this..
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does the second proof have any rule on n? like n>1?
the second proof is not true for n=1
no..
well then u cant prove the second one.... its just not true
are you sure??
let me check the given..
yeah m sure
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
2^n=n^2(2n^2-1) for n=1 which is not true
its not true for n=2 either
oops im sorry the given was wrong.. it should be 2+2^2+2^3+ . . . + 2^n = 2^(n+1) - 2
okay,... well its a very easy proof... prove true for n=1, assume true for n=k, then prove true for k+1
it is now true for n=1 right?? then? what i am going to do?
assume true for n=k
@Kira_Yamato : still i thank you..
now prove true for n=k+1
then?? i find difficulty in proof of induction :((
have u practiced any induction problems before? if u have some induction examples in ur math text book... please go thru them
all u have to do is this: prove that 2^(n+1)-2+2^(n+1)=2(n+2)-2
my teacher dont taught mathematical induction to us.. i havent encounter it before..
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
2^(n+1)-2+2^(n+1)=2^(n+2)-2 sorry i typed it up wrong before
what should i prove? if it is equal?
yes its equal... dats all u have to do for that question
oh okey.. thanks..

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