数列22+122-1，32+132-1，42+142-1，…前10项和为．

Question

数列 (22 +1)/(22 -1) ， (32 +1)/(32 -1) ， (42 +1)/(42 -1) ，…前10项和为______．

Answer 1

据题意，数列的通项为
a n =((n+1)2 +1)/((n+1)2 -1) =1+(2)/(n(n+2)) = 1+(1)/(n) -(1)/(n+2)
所以数列的前10项和为10+（ 1-(1)/(3) +(1)/(2) -(1)/(4) +(1)/(3) -(1)/(5) +…+(1)/(10) -(1)/(12) )
=10+（ 1+(1)/(2) -(1)/(11) -(1)/(12) )
=10+ (175)/(132)
=11 (43)/(132)
故答案为 11(43)/(132)