Question

3乘5分之1+5乘7分之1+7乘9分之1+……+97乘99分之1=?简便运算

Answer 1

1/(3*5)+1/(5*7)+1/(7*9)+.+1/(97*99)
=1/2*(1/3-1/5+1/5-1/7+1/7-.+1/97-1/99)
=1/2*(1/3-1/99)
=1/2*(32/99)
=16/99
1/(1*4)+1/(4*7)+1/(7*10)+.+1/(97*100)
=1/3-1/12+1/12-1/21+1/21-1/30+.+1/291-1/300
=1/3-1/300
=33/100
1/(1*5)+1/(5*9)+.+1/33/37
=1/4*(1-1/5+1/5-1/9+.+1/33-1/37)
=1/4*(1-1/37)
=9/37
顺便说一句,第三题中的第三项应该是9乘13分之1,不是9乘12分之1吧