数列777777777777777

来源：百度知道编辑：UC知道时间：2024/06/25 11:33:22

数列{an}{bn}满足anbn=1，an=n2+3n+2，则{bn}的前10项和是？

【解】:首先根据题目得知：
bn=1/an
=1/(n^2+3n+2)
=1/[(n+1)(n+2)]
=1/(n+1)-1/(n+2);
那么b1+b2+……+b10=1/2-1/3+1/3-1/4+……+1/11-1/12
=1/2-1/12
=5/12

bn=1/( n2 + 3n + 2)
=1/((n+1)(n+2))
S10=1/(2*3)+1/(3*4)....+1/(11*12)
=1/2-1/3+1/3-.....+1/11-1/12
=1/2-1/12
=5/12

bn=1/an=1/（n^2+3n+2）=1/(n+2)(n+1)=1/(n+1)-1/(n+2)
所以前10项和是1/2-1/3+1/3-1/4........+1/11-1/12=1/2-1/12=5/12

bn=1/(n+1)(n+2)
S10=1/2-1/12=5/12

5/12