2/1*4+2/4*7+2/7*10+2/10*13+.+2/(3n-2)(3n+1)

2/1*4+2/4*7+2/7*10+2/10*13+.+2/(3n-2)(3n+1)

2/(3n-2)(3n+1)=(2/3)*[1/(3n-2)-1/(3n+1)]
그래서 원 식=(2/3)*[1-1/4+1/4-1/7+1/10+1/10-13++1/(3n-2)-1/(3n+1)]
=(2/3)*[1-1/(3n+2)]
=(6n+2)/(9n+6)