Question

数列{an}中的通项公式an=1/根号n+1+根号n,Sn=9,则n=?

Answer 1

an=1/（√n+1+√n）= （√n+1-√n）/ [（√n+1+√n)（√n+1-√n]= （√n+1-√n)

Sn= √2-1+√3-√2+√4-√3……+（√n+1-√n)

= -1+√n+1 =9

即√n+1= 10

n=99