简便计算 (1+2/3)×(1-2/3)×(1+2/5)×(1-2/5)×.×(1+2
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简便计算 (1+2/3)×(1-2/3)×(1+2/5)×(1-2/5)×.×(1+2
简便计算 (1+2/3)×(1-2/3)×(1+2/5)×(1-2/5)×.×(1+2/99)×(1-2/99)
简便计算 (1+2/3)×(1-2/3)×(1+2/5)×(1-2/5)×.×(1+2/99)×(1-2/99)
(1+2/3)x(1-2/3)x(1+2/5)x(1-2/5)x...x(1+2/99)x(1-2/99)
=(1-2/3)x(1+2/3)x(1-2/5)x(1+2/5)x(1-2/7)x(1+2/7)...x(1-2/97)x(1+2/97)x(1-2/99)x(1+2/99)
=1/3 x 5/3 x 3/5 x 7/5 x 5/7 x 9/7 ...x 95/97 x 99/97 x 97/99 x 101/99
= 1/3 x 1 x 1 x 1 ...x 1 x 101/99
=1/3 x 101/99
= 101/297
=(1-2/3)x(1+2/3)x(1-2/5)x(1+2/5)x(1-2/7)x(1+2/7)...x(1-2/97)x(1+2/97)x(1-2/99)x(1+2/99)
=1/3 x 5/3 x 3/5 x 7/5 x 5/7 x 9/7 ...x 95/97 x 99/97 x 97/99 x 101/99
= 1/3 x 1 x 1 x 1 ...x 1 x 101/99
=1/3 x 101/99
= 101/297
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