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计算1/2+1/4+1/8+1/16+1/32+1/64+1/128怎么简便计算
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计算1/2+1/4+1/8+1/16+1/32+1/64+1/128怎么简便计算
▼优质解答
答案和解析
等比数列前n项和公式
1/2+1/4+1/8+1/16+1/32+1/64+1/128
=1/2+(1/2)^2+(1/2)^3+……+(1/2)^7
=1/2×[1-(1/2)^7]/(1-1/2)
=1-(1/2)^7
=1-1/128
=127/128
1/2+1/4+1/8+1/16+1/32+1/64+1/128
=1/2+(1/2)^2+(1/2)^3+……+(1/2)^7
=1/2×[1-(1/2)^7]/(1-1/2)
=1-(1/2)^7
=1-1/128
=127/128
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