简算题:2/1*3+2/3*5+2/5*7+...+2/97*99

问题描述:

简算题:2/1*3+2/3*5+2/5*7+...+2/97*99

2/3=1-1/3 2/15=1/3-1/5 2/35=1/5-1/7..
所以原式=(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+.(1/95-1/97)+(1/97-1/99)
=1/1+(-1/3+1/3)+(-1/5+1/5)-1/7+.1/95+(-1/97+1/97)-1/99
=1/1-1/99
=98/99.