數(shù)列{An}中,An=1/根號(hào)n+根號(hào)n+1.若前n項(xiàng)和Sn=9,則項(xiàng)數(shù)n等于多少?

數(shù)學(xué)人氣：505 ℃時(shí)間：2019-08-20 16:48:21

優(yōu)質(zhì)解答

an=1/[根號(hào)n+根號(hào)(n+1)]=根號(hào)(n+1)-根號(hào)n
所以a1=根號(hào)2-1
a2=根號(hào)3-根號(hào)2
a3=根號(hào)4-根號(hào)3
Sn=Σan=根號(hào)(n+1)-1=9,
所以n=99Sn=Σan=根號(hào)(n+1)-1=9是為什么？an=根號(hào)(n+1)-根號(hào)nSn=a1+a2+……+an=(根號(hào)2-1)+(根號(hào)3-根號(hào)2)+(根號(hào)4-根號(hào)3)+……+[根號(hào)(n+1)-根號(hào)n]=根號(hào)(n+1)-1