1/(3+3^1/2)+1/(5*3^1/2+3*5^1/2)+1/(7*5^1/2+5*7^1/2)+...+1/(49*47^1/2+47*49^1/2)

问题描述:

1/(3+3^1/2)+1/(5*3^1/2+3*5^1/2)+1/(7*5^1/2+5*7^1/2)+...+1/(49*47^1/2+47*49^1/2)

首先要对分母进行有理化,然后拆项相消,注意分母不要求出来要化简提取公因式原式=(3-√3)/(1*3*2)+(5√3-3√5)/(5*3*2)+(7√5-5√7)/(7*5*2)……+(49√47-47√49)/(49*47*2)=1/2(1-√3/3+√3/3-√5/5+√5/...