设数列9,99,999,9999,…的前n项和为_.

问题描述:

设数列9,99,999,9999,…的前n项和为______.

设数列9,99,999,9999,…为数列{an},其前n项和为sn
∴an=10n-1,
sn=(101+102+…+10n)-n=

10(1−10n)
1−10
-n=
10n+1−9n−10
9

故答案为:
10n+1−9n−10
9