数学简算题两道 (1)1/1*3+1/3*5+1/5*7+.+1/17*19+1/19*21 (2)1/1*2+1/2*3+1/3*4+1/4*5+.1/199*200
问题描述：
数学简算题两道 (1)1/1*3+1/3*5+1/5*7+.+1/17*19+1/19*21 (2)1/1*2+1/2*3+1/3*4+1/4*5+.1/199*200
答
(1)1/1*3+1/3*5+1/5*7+.....+1/17*19+1/19*21
=1/2(1-1/3+1/3-1/5+.....+1/17-1/19+1/19-1/21 )
=1/2(1-1/21)
=10/21
(2)1/1*2+1/2*3+1/3*4+1/4*5+.....1/199*200
=1-1/2+1/2-1/3++.....1/199-1/200
=1-1/200
=199/200
答
(1)
1/(1×3)+1/(3×5)+...+1/(17×19)+1/(19×21)
=(1/2)(1-1/3+1/3-1/5+...+1/17-1/19+1/19-1/21)
=(1/2)(1-1/21)
=10/21
(2)
1/(1×2)+1/(2×3)+...+1/(199×200)
=1-1/2+1/2-1/3+...+1/199-1/200
=1-1/200
=199/200