Question

(1-1/4)×(1-1/9)×(1-1/16)×(1-1/25)×(1-1/36)×(1-1/49)怎么简便计算

Answer 1

3/4×8/9×15/16....
分子为：1*3*2*4*3*5*4*6*5*7*6*8=1*2*3*3*4*4*5*5*6*6*7*8
分母为：2*2*3*3*4*4*5*5*6*6*7*7
最后结果为(剩下头尾)：(1*2*7*8)/(2*2*7*7)＝4/7

Answer 2

(1-1/4)×(1-1/9)×(1-1/16)×(1-1/25)×(1-1/36)×(1-1/49)

=1×3/2²×2×4/3²×3×5/4²×4×6/5²×5×7/6²×6×8/7²
=1/2×8/7
=4/7

Answer 3

平方差
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/7)(1+1/7)
=(1/2)(3/2)(2/3)(4/3)……(6/7)(8/7)
中间约分
=(1/2)(8/7)
=4/7

Answer 4

原式=（1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)(1+1/5)(1-1/5)(1+1/6)(1-1/6)(1+1/7)(1-1/7)
=3/2×1/2×4/3×2/3×5/4×3/4×6/5×4/5×7/6×5/6×8/7×6/7
=1/2×8/7
=4/7

Answer 5

=3/4×8/9×15/15×24/25×35/36×48/49
=4/7(约分)
望采纳