Mathematical Induction (1 Viewer)

[FDownes]

This question should be pretty straight forward, but I've gone through it like five times and I just can't seem to get the right solution. Could someone walk me through it so I can see what I'm doing wrong? Here's the question;

Prove, by mathematical induction, that 2/(1 x 3) + 2/(3 x 5) + 2/(5 x 7) + ... + 2/(2n - 1)(2n + 1) = 1 - 1/(2n + 1)

Please help! This is annoying the hell out of me...

 

[cwag]

sure u typed that out right buddy?

 

[tacogym27101990]

is it for all n=>1 coz n=1 isnt working for me?
its for all n=>2 yeah?
actually i agree with cwag
not sure u got the question right there mate

 

[FDownes]

Whoops, made a mistake. I've corrected it now.

Sorry guys...

 

[tacogym27101990]

ok here we go:
step 1: prove n=1
LHS = 2/3 RHS = 1 - 1/3 = 2/3
Therefore the statement is true for n = 1
step 2: assume true for n=k

2/(1X3)+2/(3X5) + ... + 2/(2k-1)(2k+1) = 1 - 1/(2k+1)

step 3: rtp n = k+1
2/(2k-1)(2k+1) + 2/(2k+1)(2k+3) = 1- 1/(2k+3)
LHS = 1 - 1/(2k+1) + 2/(2k+1)(2k+3)
= ((2k+1)(2k+3) - (2k+3) + 2
(2k+1)(2k+3)
= 4k^2+6k+2
(2k+1)(2k+3)
= (2k+1)(2k+2)
(2k+1)(2k+3)
= 2K+2
2K+3

RHS= 2k+3-1
2k+3
= 2k+2
2k+3
=LHS

 

[tacogym27101990]

sorry its pretty messy

EDIT: there we go, thats a bit better, never have bin good with neatness

 

[FDownes]

Don't worry, I can decypher it. Thanks.