[中學] 數列與級數一題

[adamchi (adamchi)]

1.設一數列<An>其前n項的和 Sn = n^2+n+3

求 (1/A1*A2) +(1/A2*A3)+......+(1/A10*A11) = _________


答: 67/440



2. 有一等差數列, 其前m項和比前n項和為 m^2:n^2

   則第m項比第n項為________

答: (2m-1):(2n-1)



3.數列<2,1,2^2,2,1,2^3,2^2,2,1,..........>則

  第一項到第405項之和為_________

答 2^29 - 31







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◆ From: 218.174.20.114
推 suhorng     :a_n = S_n - S_{n-1} = 2n for n > 1
→ suhorng     :1/a_{n+1}a_n = 1/2(1/n(n+1))=1/2(1/n-1/(n+1)),n>1