lim (n→∞)(1/2+3/2^2+5/2^3+...+(2n-1)/2^n)=?这道题下面给的做题步骤跟积分联系在一起了,还有x,怎么想也想不懂,困扰了好久,
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![lim (n→∞)(1/2+3/2^2+5/2^3+...+(2n-1)/2^n)=?这道题下面给的做题步骤跟积分联系在一起了,还有x,怎么想也想不懂,困扰了好久,](/uploads/image/z/1076932-28-2.jpg?t=lim+%EF%BC%88n%E2%86%92%E2%88%9E%EF%BC%89%EF%BC%881%2F2%2B3%2F2%5E2%2B5%2F2%5E3%2B...%2B%282n-1%29%2F2%5En%EF%BC%89%3D%3F%E8%BF%99%E9%81%93%E9%A2%98%E4%B8%8B%E9%9D%A2%E7%BB%99%E7%9A%84%E5%81%9A%E9%A2%98%E6%AD%A5%E9%AA%A4%E8%B7%9F%E7%A7%AF%E5%88%86%E8%81%94%E7%B3%BB%E5%9C%A8%E4%B8%80%E8%B5%B7%E4%BA%86%2C%E8%BF%98%E6%9C%89x%2C%E6%80%8E%E4%B9%88%E6%83%B3%E4%B9%9F%E6%83%B3%E4%B8%8D%E6%87%82%2C%E5%9B%B0%E6%89%B0%E4%BA%86%E5%A5%BD%E4%B9%85%2C)
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lim (n→∞)(1/2+3/2^2+5/2^3+...+(2n-1)/2^n)=?这道题下面给的做题步骤跟积分联系在一起了,还有x,怎么想也想不懂,困扰了好久,
lim (n→∞)(1/2+3/2^2+5/2^3+...+(2n-1)/2^n)=?
这道题下面给的做题步骤跟积分联系在一起了,还有x,怎么想也想不懂,困扰了好久,
lim (n→∞)(1/2+3/2^2+5/2^3+...+(2n-1)/2^n)=?这道题下面给的做题步骤跟积分联系在一起了,还有x,怎么想也想不懂,困扰了好久,
和积分有啥关系,差分等比数列嘛
令
Sn=1/2+3/2^2+5/2^3+...+(2n-1)/2^n,则
1/2Sn=1/2^2+3/2^3+5/2^4+...+(2n-1)/2^(n+1)
两式相减
1/2Sn=1/2+2(1/2^2+1/2^3+...+1/2^n)-(2n-1)/2^(n+1)
则
1/2Sn=1/2+1/2+1/2^2+...+1/2^(n-1)-(2n-1)/2^(n+1)
1/2Sn=1/2+1/2*[1-(1/2)^n]/(1-1/2)-(2n-1)/2^(n+1)
Sn=3-2*(1/2)^n-)-(2n-1)/2^(n+1)
则lim (n→∞)(1/2+3/2^2+5/2^3+...+(2n-1)/2^n)=
lim (n→∞)3-2*(1/2)^n-)-(2n-1)/2^(n+1)
=3
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