设A=0.1+0.11+0.111+.+0.1111111111,求A的整数部分,简便

爱你19982022-10-04 11:39:541条回答

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花落有你共回答了13个问题 | 采纳率100%: an = (1/10) +(1/10)^2 +...+(1/10)^n
Sn = a1+a2+...+an
= (1/9)( 1- (1/10)^n )
Tn= S1+S2+.+Sn
= (1/9)[ n- (1/9)( 1- (1/10)^n ) ]
A=0.1+0.11+0.111+.+0.1111111111
=T10
=(1/9)[ 10- (1/9)( 1- (1/10)^10 ) ]
=(1/9)[ 10- (1/9)( 1- (1/10)^10 ) ]
=(1/9)[ 89/9- (1/9)(1/10)^10 ) ]
A的整数部分=1; 1年前