1/(2x2-1)+1/(4x4-1)+1/(6x6-1)+-----+1/(100x100-1)=

问题描述:

1/(2x2-1)+1/(4x4-1)+1/(6x6-1)+-----+1/(100x100-1)=

1/(n^2-1)=1/2[1/(n-1)-1/(n+1)]
原式=1/2[1-1/3+1/3-1/5+.+1/99-1/101]
=1/2(1-1/101)
=50/101