2^0+2^1+2^2+2^3+``````+2^n-2怎样用公式表示
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![2^0+2^1+2^2+2^3+``````+2^n-2怎样用公式表示](/uploads/image/z/12642180-60-0.jpg?t=2%5E0%2B2%5E1%2B2%5E2%2B2%5E3%2B%60%60%60%60%60%60%2B2%5En-2%E6%80%8E%E6%A0%B7%E7%94%A8%E5%85%AC%E5%BC%8F%E8%A1%A8%E7%A4%BA)
2^0+2^1+2^2+2^3+``````+2^n-2怎样用公式表示
2^0+2^1+2^2+2^3+``````+2^n-2怎样用公式表示
2^0+2^1+2^2+2^3+``````+2^n-2怎样用公式表示
2^0=1=2^1-1
2^0+2^1=3=2^2-1
2^0+2^1+2^2=7=2^3-1
所以2^0+2^1+2^2+2^3+``````+2^(n-2)=2^(n-1)-1
可以用数字么
二进制数:111111111111111111111111111111……一共N-1个1
使用等比数列的求和公式就可以了
=(2∧(n-2)-1
设a=2^0+2^1+2^2+2^3+``````+2^(n-2),
则2a=2^1+2^2+2^3+``````+2^(n-2)+2^(n-1),
所以2a-a=2^(n-1)-2^0,
所以2^0+2^1+2^2+2^3+``````+2^(n-2)=a=2^(n-1)-1.