1/1*3+1/3*5+1/5*7+1/7*9+.+1/95*97+1/97*99=(1/1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+...+(1/97-1/99)/2=(1/1-1/3+1/3-1/5+1/5-...-1/99)/2=(1/1-1/99)/2=(98/99)/2=49/99 1/(n*(n+2))=(1/n-1/(n+2))/2