# prove by induction algebra help!

• Aug 9th 2011, 04:21 AM
university
prove by induction algebra help!
a sequece of integers x1,x2...xk..is defined recursively as follows:
x1=1 and xk+1 =xk/xk+2 for kis greater then or equal to 1
calculate x2,x3 and x4...i got
k=1:x1+1 =x1/x1+2=1/1+2=3=x^2
k=2:x2+1 =x2/x2+2=3/3+2=3=x^3
k=3:x3+1 =x3/x3+2=3/3+3=4=x^
is this right and another question using the info in the fisrt part how do i find and prove by induction a formula for the nth term xn in terms of n for all n is greater than or equal to 1,calcilate x10.
• Aug 9th 2011, 04:30 AM
Bacterius
Re: prove by induction algebra help!
Wait do you mean $\displaystyle x_{k + 1} = \frac{x_k}{x_{k + 2}}$ or $\displaystyle x_{k + 1} = \frac{x_k}{x_k} + 2$? Can you clarify please and clean up your question as it's very ambiguous right now (Doh)
• Aug 9th 2011, 04:50 AM
university
Re: prove by induction algebra help!
sorry its the first one you wrote..i didnt how to type it like you did so its a little messy sorry
• Aug 9th 2011, 04:55 AM
Siron
Re: prove by induction algebra help!
Quote:

Originally Posted by university
k=1:x1+1 =x1/x1+2=1/1+2=3=x^2
k=2:x2+1 =x2/x2+2=3/3+2=3=x^3
k=3:x3+1 =x3/x3+2=3/3+3=4=x^

This is also not clear, if $\displaystyle k=1$ then:
$\displaystyle x_2=\frac{x_1}{x_3} \Leftrightarrow x_2=\frac{1}{x_3}$

Do you mean something like this? ...
• Aug 9th 2011, 05:27 AM
university
Re: prove by induction algebra help!
well i just subbed in the numbers everwhere there was xk
• Aug 9th 2011, 05:35 AM
Bacterius
Re: prove by induction algebra help!
Quote:

well i just subbed in the numbers everwhere there was xk
$\displaystyle x_{k + 1} \ne x_k + 1$