tan−111+(1)(2)+tan−111+(2)(3)+...............+tan−111+(n−1)(n)=

We have tan-111+12+an-111+23+....+an-111+n-1n                 =tan-12-11+12+an-13-21+23+....+an-1n-n-11++n-1n                 =tan-12-tan-11+tan-13-tan-12+...+tan-1n-tan-1n-1                 =tan-1n-tan-11                 =tan-1n-11+n