求数5，55，555，…，55…5 的前n项和Sn．

∵55…5=
5
9(10n −1)
∴S_n=5+55+555+…+55…5
=
5
9[(10−1)+(102−1)+…+(10n−1)]
=
5
9[
10(10n−1)
10−1−n]
=
50
81×10n−
5
9n−
50
81