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______.
答
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=
-n=10(1−10n) 1−10
.10n+1−9n−10 9
故答案为:
.10n+1−9n−10 9