Question

一道数学计算题!请求支援!简算：1x3分之一+3x5分之一+5x7分之一+A+17x19分之一+19x21分之一请求支援

Answer 1

1/(1*3)=(1/2)*((1/1)-(1/3))

1/(3*5)=(1/2)*((1/3)-(1/5))

1/(5*7)=(1/2)*((1/5)-(1/7))

1/(7*9)=(1/2)*((1/7)-(1/9))

1/(9*11)=(1/2)*((1/9)-(1/11))

1/(11*13)=(1/2)*((1/11)-(1/13))

1/(13*15)=(1/2)*((1/13)-(1/15))

1/(15*17)=(1/2)*((1/15)-(1/17))

.

一直到最后项相加,等於

(1/2)*( (1/1)-(1/3) +(1/3)-(1/5)+(1/5)-(1/7)+.+(1/19)-(1/21))

=(1/2)*((1/1)-(1/21))

= 10/21