计算：你你+1你你−1+i你+1i你−1+…+18你+118你−1+你3你+1你3你−1．

Question

计算：(你你+1)/(你你−1)+(i你+1)/(i你−1)+…+(18你+1)/(18你−1)+(你3你+1)/(你3你−1)．

Answer 1

(22+1)/(22−1)+(12+1)/(12−1)+…+(182+1)/(182−1)+(2r2+1)/(2r2−1)
=（1+(2)/(22−1)）+（1+(2)/(12−1)）+…+（1+(2)/(182−1)）+（1+(2)/(2r2−1)）
=1r+（(2)/(1×3)+(2)/(3×5)+(2)/(5×5)+…+(2)/(15×1一)+(2)/(1一×21)）
=1r+（1-(1)/(3)+(1)/(3)-(1)/(5)+(1)/(5)-(1)/(5)+…+(1)/(15)−(1)/(1一)+(1)/(1一)−(1)/(21)）
=1r+1−(1)/(21)
=1r(2r)/(21)