用简便方法计算．150×51+151×52+152×53+153×54+154×55．

Question

用简便方法计算．
(1)/(50×51)+(1)/(51×52)+(1)/(52×53)+(1)/(53×54)+(1)/(54×55)．

Answer 1

(1)/(50×51)+(1)/(51×52)+(1)/(52×53)+(1)/(53×54)+(1)/(54×55)
=(1)/(50)-(1)/(51)+(1)/(51)-(1)/(52)+(1)/(52)-(1)/(53)+(1)/(53)-(1)/(54)+(1)/(54)-(1)/(55)
=(1)/(50)-(1)/(55)
=(5)/(2750)
=(1)/(550)．