masterpeace什么意思:简便运算

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2/2*4+2/4*6+2/6*8+……+2/98*100

(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*(1+1/4)*(1-1/4)*……*(1+1/99)*(1-1/99)*(1+1/100)*(1-100)

2/2*4=2/2-2/4
2/4*6=2/4-2/6
2/6*8=2/6-2/8
……

2/2*4+2/4*6+2/6*8+……+2/98*100 =2/2-2/100=49/50

(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*(1+1/4)*(1-1/4)*……*(1+1/99)*(1-1/99)*(1+1/100)*(1-100)=
(1+1/2)*(1+1/3)*……*(1+1/99)(1+1/100)*(1-1/2)*(1-1/3)*(1-1/99)*(1-1/100)=
(3/2×4/3×4/5×……×100/99×101/100)×(1/2*2/3*3/4*98/99*99/100)=
101/2×1/100=101/200

2/2*4=(4-2)/2*4=1/2-1/4;
接下去自己想
第2题提示:
每两项化成(n-1)*(n+1)/(n*n)

2/2*4
2/(2*4)

2/2*4=2/2-2/4
2/4*6=2/4-2/6
2/6*8=2/6-2/8
……

2/2*4+2/4*6+2/6*8+……+2/98*100 =2/2-2/100=49/50

(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*(1+1/4)*(1-1/4)*……*(1+1/99)*(1-1/99)*(1+1/100)*(1-100)=
(1+1/2)*(1+1/3)*……*(1+1/99)(1+1/100)*(1-1/2)*(1-1/3)*(1-1/99)*(1-1/100)=
(3/2×4/3×4/5×……×100/99×101/100)×(1/2*2/3*3/4*98/99*99/100)=
101/2×1/100=101/200