f(x+1)= f(x)+x F(1)=4 ise. f(20)=?

Given the functional equation f(x+1) = f(x) + x and f(1) = 4, we can find f(20) by repeatedly applying the functional equation.

First, we find f(2):
f(2) = f(1+1) = f(1) + 1 = 4 + 1 = 5

Next, we find f(3):
f(3) = f(2+1) = f(2) + 2 = 5 + 2 = 7

Continuing this process, we find f(4), f(5), and so on until we find f(20).

f(4) = f(3+1) = f(3) + 3 = 7 + 3 = 10
f(5) = f(4+1) = f(4) + 4 = 10 + 4 = 14
f(6) = f(5+1) = f(5) + 5 = 14 + 5 = 19
f(7) = f(6+1) = f(6) + 6 = 19 + 6 = 25
\vdots
f(20) = f(19+1) = f(19) + 19 = \textbf{194}

Therefore, f(20) = \boxed{194}.