一个数列问题

若Sn=1/(1*4)+1/(4*7)+......+1/[(3n-2)(3n+1)],则Sn的值为?

热心网友

Sn=(1/3)(1-1/4)+3(1/4-1/7)+.......+3[1/(3n-2)-1/(3n+1)]=[1-1/4+1/4-1/7+....+1/(3n-2)-1/(3n+1)]/3=[1-1/(3n+1)]/3=n/(3n+1)

热心网友

S=[1-1/4+1/4-1/7+ ......+1/(3N-2)-1/ (3N+1)]/3==[1-1/ (3N+1)]/3=N/3N+1