1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102=?

题目

1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102=?

答案

∵2*【1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102】
=1/1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+.+1/99-1/101+1/100-1/102
=1+1/2-1/101-1/102
=(101*102+101*51-102-101)/101*102
=15250/10302
=7625/5151
∴ 1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102=12=7625/10302