3的0次方+3的1次方+3的2次方0...+3的n次方>10的7次方，求n最小整數為多少?
回答 (2)
2015-12-27 8:59 am
a=3^0
r=3^1/3^0=3
3的0次方+3的1次方+3的2次方0...+3的n次方>10的7次方
(3^0)(3-1)^n /(3-1)>10^7
2^n>2000000
nlog2>log20000000
n>24.25349666
n最小整數為25
r=3^1/3^0=3
3的0次方+3的1次方+3的2次方0...+3的n次方>10的7次方
(3^0)(3-1)^n /(3-1)>10^7
2^n>2000000
nlog2>log20000000
n>24.25349666
n最小整數為25
2015-12-27 6:03 am
Sol
A=3^0+3^1+3^2+…+3^n
3A=3^1+3^2+3^3_...+3^(n+1)
2A=3^(n+1)－1
3^(n+1)－1>2*10^7
3^(n+1)>2*10^7+1
(n+1)log3>7+log2
(n+1)*0.4771>7.3010
n+1>15.303
n>14.303
n>=15
A=3^0+3^1+3^2+…+3^n
3A=3^1+3^2+3^3_...+3^(n+1)
2A=3^(n+1)－1
3^(n+1)－1>2*10^7
3^(n+1)>2*10^7+1
(n+1)log3>7+log2
(n+1)*0.4771>7.3010
n+1>15.303
n>14.303
n>=15
收錄日期: 2021-04-18 14:13:49
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20151226193516AAZprzU