Solve the difference equation y_{n+1}=(n+1)/(n+2) y_{n} in terms of the initial value y_{0}.
Answer: y_{n}=y_{0}/(n+1)
Solve the difference equation y_{n+1}=(n+1)/(n+2) y_{n} in terms of the initial value y_{0}.
Answer: y_{n}=y_{0}/(n+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]y_{0}, up to n = 1
= [1/(n+2)]y_{0}, after canceling out (n+1)!
or
y_{n} = [1/(n+1)]y_{0},_{ }if you substitute n for n+1.