polynomials - How do I prove this math rule? -

the given information is:

f(1)=1/2  f(2)=f(1)+2/(2*2)  f(3)=f(2)+3/(2*2*2)  f(4)=f(3)+4/(2*2*2*2) ... f(n)=f(n-1)+n/(2^n) 

how prove

 f(n) < 2 ? 

and sum on n*q^n

q/(1-q)^2 

now set q=0.5 2 limit value steadily increasing sequence tends to, never reaches.