For a certain function f(n), the identity
(2n)/n - (2n)/(n + 1) = f(n) (2n)/n
for all nonnegative integers n. Find f(n).
+132 The f(n) = 1/(n+1) is the simplified form of the function.
(2n)/n - (2n)/(n + 1) = f(n) (2n)/n
Simplifying:
(2n)/n - (2n)/(n + 1) = 2f(n)
(2n)/2n - (2n)/2(n + 1) = 2f(n)/2
1 - n/(n+1) = f(n)
(n+1 - n)/(n+1) = f(n)
1/(n+1) = f(n)
