求和:(1)Sn=1+(1+2)+(1+2+2的平方)+……+(1+2+2的平方...+2的n-1次方)(2)Sn=(1/2的2次方-1)+(1/4的2次方-1)+(1/6的2次方-1)+...+1/(2n)的平方-1
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![求和:(1)Sn=1+(1+2)+(1+2+2的平方)+……+(1+2+2的平方...+2的n-1次方)(2)Sn=(1/2的2次方-1)+(1/4的2次方-1)+(1/6的2次方-1)+...+1/(2n)的平方-1](/uploads/image/z/600561-9-1.jpg?t=%E6%B1%82%E5%92%8C%EF%BC%9A%EF%BC%881%EF%BC%89Sn%3D1%2B%EF%BC%881%2B2%EF%BC%89%2B%EF%BC%881%2B2%2B2%E7%9A%84%E5%B9%B3%E6%96%B9%EF%BC%89%2B%E2%80%A6%E2%80%A6%2B%EF%BC%881%2B2%2B2%E7%9A%84%E5%B9%B3%E6%96%B9...%2B2%E7%9A%84n-1%E6%AC%A1%E6%96%B9%EF%BC%89%282%29Sn%3D%EF%BC%881%2F2%E7%9A%842%E6%AC%A1%E6%96%B9-1%EF%BC%89%2B%EF%BC%881%2F4%E7%9A%842%E6%AC%A1%E6%96%B9-1%EF%BC%89%2B%EF%BC%881%2F6%E7%9A%842%E6%AC%A1%E6%96%B9-1%EF%BC%89%2B...%2B1%2F%EF%BC%882n%EF%BC%89%E7%9A%84%E5%B9%B3%E6%96%B9-1)
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求和:(1)Sn=1+(1+2)+(1+2+2的平方)+……+(1+2+2的平方...+2的n-1次方)(2)Sn=(1/2的2次方-1)+(1/4的2次方-1)+(1/6的2次方-1)+...+1/(2n)的平方-1
求和:(1)Sn=1+(1+2)+(1+2+2的平方)+……+(1+2+2的平方...+2的n-1次方)
(2)Sn=(1/2的2次方-1)+(1/4的2次方-1)+(1/6的2次方-1)+...+1/(2n)的平方-1
求和:(1)Sn=1+(1+2)+(1+2+2的平方)+……+(1+2+2的平方...+2的n-1次方)(2)Sn=(1/2的2次方-1)+(1/4的2次方-1)+(1/6的2次方-1)+...+1/(2n)的平方-1
通项公式
a(n) = 1 + 2 + 2^2 + ...+ 2^(n-1) = 2^n - 1,n = 1,2,...
S(n) = a(1) + a(2) + ...+ a(n)
= 2^1 - 1 + 2^2 - 1 + ...+ 2^n - 1
= 2[1 + 2 + ...+ 2^(n-1)] - n
= 2[2^n - 1] - n
= 2^(n+1) - n - 2,
(n = 1,2,...)
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