阿摩線上測驗
4. 求
= 。
詳解 (共 1 筆)
詳解
[1+1/(2-1)(2+1)][1+1/(3-1)(3+1)]...[1+1/(111-1)(111+1)]
=[22/(22-1)][32/(32-1)]...[1112/(1112-1)]
=(2x3x...x111)2/ (2-1)(3-1)...(111-1)(2+1)(3+1)...(111+1)
=(2x3x...x111)2/ (1x2x3x...x110)(3x4x...x112)
=(2x3x...x111)2 / (2x111x112)(3x4x...x110)2,
=(2x111)2 / (2x111x112)
=(2x111)/112
=111/56