求下列数列的极限：lim(n→∞) [1/(2*5)+1/(5*8)+1/(8*11)+……+1/(3n-1)*(3n+2)]那个_数学解答

求下列数列的极限：lim(n→∞) [1/(2*5)+1/(5*8)+1/(8*11)+……+1/(3n-1)*(3n+2)]
那个……老师给的答案是1/6的说……请问，后面的数列求和是怎么出来的呢？

人气：243 ℃　时间：2020-02-03 09:31:45

解答

1/(2*5)+1/(5*8)+1/(8*11)+……+1/(3n-1)*(3n+2)]
=1/3[1/2-1/5+1/5-1/8+1/8-1/11+……+1/(3n-1)-1/(3n+2)]
=1/3[1/2-1/(3n+2)]
lim(n→∞) 1/3[1/2-1/(3n+2)]=1/6