Question

S=1/2+1/6+1/12+...+1/(n^2+n)

Answer 1

S=1/1-1/2+1/2-1/3+1/3-1/4+...+1/(n-1)-1/n+1/n-1/(n+1)=1/1-1/(n+1)=(n+1-1)/(n+1)=n/(n+1)

fractiile de tipul 1/n(n+1) =1/n-1/(n+1)