2²/1×3+4²/3×5+6²/5×7+…+20²/19×21怎么简算?

2²/1×3+4²/3×5+6²/5×7+…+20²/19×21怎么简算?
2²/1×3+4²/3×5+6²/5×7+…+20²/19×21怎么简算?

2²/1×3+4²/3×5+6²/5×7+…+20²/19×21怎么简算?
2²/1×3+4²/3×5+6²/5×7+…+20²/19×21
=1+1/1x3+1+1/3x5+1+1/5x7+...+1+1/19x21
=1x19+1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+...+1/2(1/19-1/21)
=19+1/2(1-1/21)
=19+10/21
=19又10/21