Question

i need help ..

Answer 1

@Bugay♥ Hi :)
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Answer 2

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)

Answer 3

thanks @hartnn ..

Answer 4

Satisfy by k
Satisfy by k+1

Answer 5

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

Answer 6

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

Answer 7

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 .

Answer 8

3 is divisible by 3
then?

Answer 9

??

Answer 10

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

Answer 11

i am sorry, i keep on getting disconnected..

Answer 12

oh its ok..

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

@Tushara : hello..

Answer 18

@hartnn : its okey thank you so much..

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

the second proof is not true for n=1

Answer 23

no..

Answer 24

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

Answer 25

are you sure??

Answer 26

let me check the given..

Answer 27

yeah m sure

Answer 28

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

Answer 29

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

Answer 30

its not true for n=2 either

Answer 31

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

Answer 32

okay,... well its a very easy proof... prove true for n=1, assume true for n=k, then prove true for k+1

Answer 33

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

Answer 34

assume true for n=k

Answer 35

@Kira_Yamato : still i thank you..

Answer 36

now prove true for n=k+1

Answer 37

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

Answer 38

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

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

2^(n+1)-2+2^(n+1)=2^(n+2)-2

sorry i typed it up wrong before

Answer 43

what should i prove? if it is equal?

Answer 44

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

Answer 45

oh okey.. thanks..