1/(√3+1)+1/(√5+√3)+1/(√7+√5)+.+1/√2n+1+√2n+1怎么化简
问题描述:
1/(√3+1)+1/(√5+√3)+1/(√7+√5)+.+1/√2n+1+√2n+1怎么化简
答
1/(√3+1)+1/(√5+√3)+1/(√7+√5)+.+1/√2n+1+√2n-1
=(√3-1+√5-√3+√7-√5+……+(√2n+1)-√(2n-1))/2
=(√(2n+1)-1)/2