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.


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