5+55+555+5555+······+55······55 ｛2010个5｝求和_数学解答

5+55+555+5555+······+55······55 ｛2010个5｝求和

人气：415 ℃　时间：2020-04-17 22:19:00

解答

Sn=5+55+555+……+55……55(n个5)
=5*[1+11+111+……+11……11(n个1)]
=5/9*[9+99+999+……+99……99(n个9)]
=5/9(10-1+100-1+1000-1+……+10^n-1)
=5/9[10*(1-10^n)/(1-10)-n]
=5/81*[10^(n+1)-9n-10]
S2010=5/81*(10^2011-18100)