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alright i dno where to start... this is probably much harder then what Crimson posted but still

Show that 1/r! - 1/(r+1)! = r/(r+1)!

and if some1 asks. r is any number... r doesnt equal something specifically.

if you need another clue i know it has something to do with proof by induction

good luck

thanks in advance too this is in meh homework for half term
EDIT:

HENCE find an expression, in terms of n, for
1/2! + 2/3! +3/4!+......+n/(n+1)!

I havent been in school in a while whats "!" stand for?

! is factorial. So 4! = 4*3*2*1.

o ****, have fun man.

penfold1992 wrote: Show that 1/r! - 1/(r+1)! = r/(r+1)!

multyply 1/r! with r+1 and u ll have r+1/(r+1)!

and r+1/(r+1)! - 1/(r+1)! its r/(r+1)! . simple no ?:O

only_me wrote:

penfold1992 wrote: Show that 1/r! - 1/(r+1)! = r/(r+1)!

multyply 1/r! with r+1 and u ll have r+1/(r+1)!

and r+1/(r+1)! - 1/(r+1)! its r/(r+1)! . simple no ?:O

if you multiply 1/r! with r+1 you'll get r+1/r! , no ?

only_me wrote:

penfold1992 wrote: Show that 1/r! - 1/(r+1)! = r/(r+1)!

multyply 1/r! with r+1 and u ll have r+1/(r+1)!

and r+1/(r+1)! - 1/(r+1)! its r/(r+1)! . simple no ?:O

u need that for the HENCE bit.. which is what i cant do lol
that bits fine for me. its the other bit
i missed it out when i wrote problem but thats my fault -.-

and to that above me...
he ment multiply with r+1/r+1 because thats 1.. its a equal fraction so its ok

the answer is 4.

the answer is: true.

.AWAKE. wrote:the answer is 4.

you forgot to carry the 1.

r = 1.

1/1-1/(1+1)=1/(1+1)

so 2/2 - 1/2 = 1/2.

Permutations suck. Junior year was great though. Babs taught me...well, nothing i remember.

Blindfire wrote:r = 1.

1/1-1/(1+1)=1/(1+1)

so 2/2 - 1/2 = 1/2.

thats surprisingly simple...

1.1?

Blindfire wrote:r = 1.

1/1-1/(1+1)=1/(1+1)

so 2/2 - 1/2 = 1/2.

That's what I got too. But there could be more numbers which fulfil the formula so I wonder if solving one variable is enough.

DumboDii wrote:

Blindfire wrote:r = 1.

1/1-1/(1+1)=1/(1+1)

so 2/2 - 1/2 = 1/2.

That's what I got too. But there could be more numbers which fulfil the formula so I wonder if solving one variable is enough.

it works for all whole numbers above 0 at least. -.- it didnt prove it at all it just showed that it was true.

put 98363928692038694 as r and i bet you get the same outcome -.-

the reason is... because a PROOOF shows that. thats why the proof was necesarry before you do the 2nd part of the question.
proof by induction. kudos to any1 who actually does it rather then puts numbers into a formula already known to be true. also if it wasnt true why would it have a equal sign there?

penfold1992 wrote:

DumboDii wrote:

Blindfire wrote:r = 1.

1/1-1/(1+1)=1/(1+1)

so 2/2 - 1/2 = 1/2.

That's what I got too. But there could be more numbers which fulfil the formula so I wonder if solving one variable is enough.

it works for all whole numbers above 0 at least. -.- it didnt prove it at all it just showed that it was true.

put 98363928692038694 as r and i bet you get the same outcome -.-

the reason is... because a PROOOF shows that. thats why the proof was necesarry before you do the 2nd part of the question.
proof by induction. kudos to any1 who actually does it rather then puts numbers into a formula already known to be true. also if it wasnt true why would it have a equal sign there?

Proof by induction is different than just proving an equation with variables. There are 2 main parts:
1)Prove the base case (the first case aka n=0)
2)Assuming the nth (any n) case is true, prove the (n+1)st case is also true

He proved it, just not by induction.

1/1! - 1/2! = 1/2!
1 - 1/2 = 1/2
1/2 = 1/2 => 1

1/R! - 1/(R+1)! = R/(R+1)!
(R+1)!/R! - (R+1)!/(R+1)! = R
(R+1) - 1 = R
R = R => 1

1/(R+1)! - 1/(R+2)! = (R+1)/(R+2)!
(R+2)!/(R+1)! - (R+2)!/(R+2)! = R+1
(R+2) - 1 = R+1
R+1 = R+1 => 1

-----------------------------------

∑ n/(n+1)! = ∑ [n+1-1/(n+1)!] = ∑ [(n+1)/(n+1)!] - ∑ [1/(n+1)!] = ∑ (1/n!) - ∑ [1/(n+1)!] =
∑ [1/n! - 1/(n+1)!] -> telescopic series

(1/1! - 1/2!) + (1/2! - 1/3!) + (1/3! - 1/4!) + ... + (1/n! - 1/(n+1)!) = .. (note: bold terms means they cancel)
1/1! - 1/(n+1)! = 1 - 1/(n+1)!

I fcking hate math.

KillAndChill wrote:Proof by induction is different than just proving an equation with variables. There are 2 main parts:
1)Prove the base case (the first case aka n=0)
2)Assuming the nth (any n) case is true, prove the (n+1)st case is also true

He proved it, just not by induction.

hmm i see what you mean... but the sum of series between r=1 and n of
r/(r+1)! cannot be solved by proving it in the way he did.

seeing as you know what proof by induction is.. (unless u googled it haha)
wna give it a go ... at least thats what i think needs to be done :S
summing series requires proof by induction? hmm cant be right... maybe summing of 1/x and such... **** FURTHER MATHS! WHY DID I TAKE IT!

http://answers.yahoo.com/dir/index;_ylt ... =396545161

np

penfold1992 wrote:

KillAndChill wrote:Proof by induction is different than just proving an equation with variables. There are 2 main parts:
1)Prove the base case (the first case aka n=0)
2)Assuming the nth (any n) case is true, prove the (n+1)st case is also true

He proved it, just not by induction.

hmm i see what you mean... but the sum of series between r=1 and n of
r/(r+1)! cannot be solved by proving it in the way he did.

seeing as you know what proof by induction is.. (unless u googled it haha)
wna give it a go ... at least thats what i think needs to be done :S
summing series requires proof by induction? hmm cant be right... maybe summing of 1/x and such... **** FURTHER MATHS! WHY DID I TAKE IT!

I would do it, but I hate it. It was a big part of my test today and I don't wanna ever do it again, lol.

hahaha this subject is absolute shite right? thats why i posted, i cant be asked with this stupid subject anymore xD

i saw series in highschool and during integral calculus in the university, it was clearly the lighter and easier part of the subject lol. if you think summing series is shit, once you see diferential equations or multivariable calculus you will pull your ball hairs out!