Thread: 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.

Wait do you mean or ? Can you clarify please and clean up your question as it's very ambiguous right now

sorry its the first one you wrote..i didnt how to type it like you did so its a little messy sorry

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 then:


Do you mean something like this? ...

well i just subbed in the numbers everwhere there was xk

well i just subbed in the numbers everwhere there was xk