anonymous
  • anonymous
i need help ..
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
hartnn
  • 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 :)
anonymous
  • anonymous
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)
anonymous
  • anonymous
thanks @hartnn ..

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.