Solve the difference equation?

Question

Solve the difference equation y_n+1=(n+1)/(n+2) y_n in terms of the initial value y₀.

Answer: y_n=y₀/(n+1)

Answer 1

y_n+1

= [(n+1)/(n+2)]y_n

= [(n+1)/(n+2)][n/(n+1)]y_n-1

= [(n+1)/(n+2)][n/(n+1)]...[1/2]y₀, up to n = 1

= [1/(n+2)]y₀, after canceling out (n+1)!

or

y_n = [1/(n+1)]y₀, if you substitute n for n+1.

Answer 2

I answered the same questions two days ago. See link:

https://www.wyzant.com/answers/12033/solve_the_difference_equation