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求数5,55,555,…,55…5 的前n项和Sn
人气:190 ℃ 时间:2020-09-19 09:10:37
解答
∵55…5=
5
9
(10n −1)

∴Sn=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
9
n−
50
81
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