Question

利用因式分解计算(1-1/2的2次方)(1-1/3的2次方)(1-1/4的2次方)(1-1/5的2次方)

Answer 1

(1-1/2的2次方)(1-1/3的2次方)(1-1/4的2次方)(1-1/5的2次方)
=(1 + 1/2)(1 - 1/2)(1 + 1/3)(1 - 1/3)(1 + 1/4)(1 - 1/4)(1 + 1/5)(1 - 1/5)
=(3/2)*(1/2)*(4/3)*(2/3)*(5/4)*(3/4)*(6/5)*(4/5)
=[(3/2)*(4/3)*(5/4)*(6/5)]*[(1/2)*(2/3)*(3/4)*(4/5)]
=3* 1/5
=3/5

Answer 2

(1-1/2的2次方)(1-1/3的2次方)(1-1/4的2次方)(1-1/5的2次方)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)(1+1/5)(1-1/5)
=3/2*1/2*4/3*2/3*5/4*3/4*6/5*4/5
=....

Answer 3

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

Answer 4

分解后 为（1-1/2）×（1+1/2）×（1-1/3）×（1+1/3）×……×（1-1/5）×（1+1/5）
=1/2×3/2×2/3×4/3×……×4/5×6/5=3/5

Answer 5

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)
=3/2乘1/2乘4/3乘2/3乘5/4乘3/4乘6/5乘4/5
=1/2乘6/5
=3/5