等差數列求和急 1/1+1/(1+2)+1/(1+2+3).+1/(1+2+3+..N)

等差數列求和急 1/1+1/(1+2)+1/(1+2+3).+1/(1+2+3+..N)

原式=1+2/2*(2+1)+2/3*(3+1)+……+2/n(n+1)
=1+2(1/2-1/3+1/3-1/3+……+1/n-1/(n+1)
=1+1/4-1/2(n+1)
=(3-2n)/4(n+1)