1+2+2的平方+2的立方+2的(立方+1)·····+2的(立方+9)要过程1+2+2的平方+2的立方+2的(立方+1)················2的(立方+6)前面错了
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![1+2+2的平方+2的立方+2的(立方+1)·····+2的(立方+9)要过程1+2+2的平方+2的立方+2的(立方+1)················2的(立方+6)前面错了](/uploads/image/z/991876-4-6.jpg?t=1%2B2%2B2%E7%9A%84%E5%B9%B3%E6%96%B9%2B2%E7%9A%84%E7%AB%8B%E6%96%B9%2B2%E7%9A%84%EF%BC%88%E7%AB%8B%E6%96%B9%2B1%EF%BC%89%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%2B2%E7%9A%84%EF%BC%88%E7%AB%8B%E6%96%B9%2B9%EF%BC%89%E8%A6%81%E8%BF%87%E7%A8%8B1%2B2%2B2%E7%9A%84%E5%B9%B3%E6%96%B9%2B2%E7%9A%84%E7%AB%8B%E6%96%B9%2B2%E7%9A%84%EF%BC%88%E7%AB%8B%E6%96%B9%2B1%EF%BC%89%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B72%E7%9A%84%EF%BC%88%E7%AB%8B%E6%96%B9%2B6%EF%BC%89%E5%89%8D%E9%9D%A2%E9%94%99%E4%BA%86)
1+2+2的平方+2的立方+2的(立方+1)·····+2的(立方+9)要过程1+2+2的平方+2的立方+2的(立方+1)················2的(立方+6)前面错了
1+2+2的平方+2的立方+2的(立方+1)·····+2的(立方+9)
要过程
1+2+2的平方+2的立方+2的(立方+1)················2的(立方+6)前面错了
1+2+2的平方+2的立方+2的(立方+1)·····+2的(立方+9)要过程1+2+2的平方+2的立方+2的(立方+1)················2的(立方+6)前面错了
这是个等比数列求和问题.S=(1-2^10)/(1-2)=2^10-1=1023
直接用等比公式计算就可以了
n = 1, S = 2^0 = 1
n = 2, S = 2^0 + 2^1 = 1 + 2 = 3
n = 3, S = 2^0 + 2^1 + 2^2 = 1 + 2 + 4 = 7
n = 4, S = 2^0 + 2^1 + 2^2 + 2^3 = 1 + 2 + 4 + 8 = 15
n = n, S = 2^0 + 2^1 + 2^2 + 2^3 + ...
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n = 1, S = 2^0 = 1
n = 2, S = 2^0 + 2^1 = 1 + 2 = 3
n = 3, S = 2^0 + 2^1 + 2^2 = 1 + 2 + 4 = 7
n = 4, S = 2^0 + 2^1 + 2^2 + 2^3 = 1 + 2 + 4 + 8 = 15
n = n, S = 2^0 + 2^1 + 2^2 + 2^3 + ....+ 2^(n-2) + 2^(n-1)
2S = 2 * (2^0 + 2^1 + 2^2 + 2^3 + .... + 2^(n-1)) = 2^1 + 2^2 + 2^3 + ....+ 2^(n-1) + 2^n
=>
S = 2S - S = 2^1 + 2^2 + 2^3 + .... + 2^n - (2^0 + 2^1 + 2^2 + 2^3 + .... + 2^(n-1)) = 2^n - 1
S = 2^0 + 2^1 + 2^2 + 2^3 + .... + 2^(n-1) = 2^n - 1
1+ 2^2 + 2^3 + ..... + 2^9 => n-1 = 9
n = 10 =>S = 2^10 - 1 = 1023
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