Question

求简便计算法和过程!1乘5（分子）分之4+5乘9（分子）之4+9乘13（分子）之4+13乘17（分子）之4+17乘21（

Answer 1

1x(4/5)+5x(4/9)+9x(4/13)+13x(4/17)+17x(4/21)

=4x[(1/5)+(5/9)+(9/13)+(13/17)+(17/21)]

=4x[1-(4/5）+1-（4/9）+1-（4/13）+1-（4/17）+1-（4/21）]

=4x5-4x4x[(1/5)+(1/9)+(1/13)+(1/17)+(1/21)]

=20-16x[9x13x17x21+5x13x17x21+5x9x17x21+5x9x13x21+5x9x13x17]/(5x9x13x17x21)

=20-16x(87204/208845)

=20-1395264/208845

=(4176900-1395264)/208845

=2781636/208845