Let-f-and-g-be-functions-such-that-for-all-real-number-x-and-y-g-f-x-y-f-x-x-y-g-y-Find-the-value-of-g-0-g-1-g-2-g-3-g-2016-

Question Number 4702 by 314159 last updated on 22/Feb/16

Let f and g be functions such that for all

real number x and y, g (f (x + y)) = f (x) + (x + y) g (y) .

Find the value of g (0) + g (1) + g (2) + g (3) + \dots + g (2016) .

Commented by prakash jain last updated on 22/Feb/16

Let us try for trivial solution

f (x) = g (x) = 0

Trivial solution satisfies the given condition

for all x, y \in R

so \underset{i = 0}{\sum^{2016}} g (i) = 0

If there is a unique solution for the sum in

question then it must be equal to 0 .