求数列0.9,0.99,0.999,...,{0. - 知识问答

求数列0.9,0.99,0.999,...,{0.99...9...}(n个9)前n项和.

1个回答

Sn=0.9+0.99+0.999+.+{0.99.9}(n个9)
=1-0.1+1-0.01+1-0.001+.+1-0.0.1}(n个0)
=n-[(1/10)+(1/10)^2 +.+(1/10)^n]
=n-[1/10 -(1/10)^(n+1)]/(1-1/10)
=n-1/9 [1-(1/10)^n]
=n-(1-1/10^n)/9

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