Question

1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+ …+1/(93*95*97)+1/(95*97*99)＝多

Answer 1

1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+ …+1/(93*95*97)+1/(95*97*99)

= (1/4)*[1/(1*3) - 1/(3*5)] + (1/4)*[1/(3*5) - 1/(5*7)] + ... + (1/4)*[1/(95*97) - 1/(97*99)]

= (1/4)*[1/(1*3) - 1/(97*99)]

= 800/9603