如果,n是大于2的整数,计算1/(n-1)(n-2)+1/(n-2)(n-3)+1/(n-3)(n-4)+……+1/(n-2010)(n-2011)

问题描述:

如果,n是大于2的整数,计算1/(n-1)(n-2)+1/(n-2)(n-3)+1/(n-3)(n-4)+……+1/(n-2010)(n-2011)

1/(n-1)(n-2)+1/(n-2)(n-3)+1/(n-3)(n-4)+……+1/(n-2010)(n-2011)=-1/(n-1)+1/(n-2)-1/(n-2)+1/(n-3)-1/(n-3)+1/(n-4)-...-1/(n-2010)+1/(n-2011).裂项=-1/(n-1)+1/(n-2011).消去中间项=-(n-2011-n+1)/(n-1)(n-2011...