3條數學(10),唔要亂答

答案正確，但實在看得眼花。 @_@
abcsghk的回答比較易看易明。

支持你
因為我完全睇唔明所以冇答到
你居然咁都答到
勁!!

1.
(1 - 1/10²)*(1 - 1/11²)*(1 - 1/12²)*(1 - 1/13²)*(1 - 1/14²)*(1 - 1/15²)
= (10² - 1)/10² * (11²-1)/11² * (12²-1)/12² * (13²-1)/13² * (14²-1)/14² * (15²-1)/15² 【每個括號內通分母】
= (10-1)(10+1)/10² * (11-1)(11+1)/11² * (12-1)(12+1)/12² * (13-1)(13+1)/13² * (14-1)(14+1)/14² * (15-1)(15+1)/15²【因為 a²-b² = (a-b)(a+b)】
= (9*11/10²)*(10*12/11²)*(11*13/12²)*(12*14/13²)*(13*15/14²)*(14*16/15²)【分子分母約簡】
= 9/10 * 16/15
= 144/150
= 24/25


2.
(1-1/2+1/3-1/4+...+1/19-1/20) / (1/440+1/480+...+1/760+1/800)
= (1-1/2+1/3-1/4+...+1/19-1/20) / [1/40 (1/11+1/12+...+1/19+1/20)]【分母每項抽出1/40】
= [(1+1/2+1/3+1/4+...+1/19+1/20) - 2*(1/2+1/4+1/6+...+1/20)] / [1/40 (1/11+1/12+...+1/19+1/20)]【為分子補上項令其變成全加，但要於後面減回2倍的項】
= [(1+1/2+1/3+1/4+...+1/19+1/20) - (1+1/2+1/3+...+1/10)] / [1/40 (1/11+1/12+...+1/19+1/20)]【將2乘進括號內】
= (1/11+1/12+1/13+...+1/19+1/20) / [1/40 (1/11+1/12+...+1/19+1/20)]【相減後只餘下尾項】
= 1 / (1/40)【分子分母約簡相同項】
= 40


3.
2+1/2+0.039/[1/20*(2.31/0.077)]-2.526
= 2+1/2+0.039/[1/20*(2310/77)]-2.526
= 2+1/2+0.039/[1/20*30]-2.526
= 2+1/2+0.039/[3/2]-2.526
= 2+1/2+0.039*2/3-2.526
= 2+1/2+0.039/3*2-2.526
= 2+1/2+0.013*2-2.526
= 2+1/2+0.026-2.526
= 2.5+0.026-2.526
= 2.526-2.526
= 0


希望幫倒你！^^

(1-1/10²)*(1-1/11²)*(1-1/12²)*(1-1/13²)*(1-1/14²)*(1-1/15²)
=[(10²-1)/10²][(11²-1)/11²][(12²-1)/12²][(131²-1)/13²][(14²-1)/14²][(15²-1)/15²]
=[(9)(11)/10²][(10)(12)/11²][(11)(13)/12²][(12)(14)/13²][(13)(15)/14²][(14)(16)/15²]
=[9(10)(11²)(12²)(13²)(14²)(15)(16)]/(10²)(11²)(12²)(13²)(14²)(15²)
=9(16)/10(15)
=144/150
=0.96

(1-1/2+1/3-1/4+...+1 /19-1/20)/(1/440+1/4 80+...+1/760+1/800)
=唔知,sorry...
2+1/2+0.039/[1/20*(2.31/0.077)]-2.526
=2.5 + 0.039(1/20 * 30) - 2.526
=0.039(1.5) - 0.026
=0.013(4.5-2)
=0.013(2.5)
=0.0325

1. 0
2. 0
3. -1.487