作业帮已知数列｛an｝中,an=2^[(n-1)/2]n为奇数,an=2^(-n/2)n为偶数,则an的前2n项和为?已知数列｛an｝中,an=｛2^[(n-1)/2] n为奇数, 2^(-n/2) n为偶数,则an的前2n项和为?
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![已知数列｛an｝中,an=2^[(n-1)/2]n为奇数,an=2^(-n/2)n为偶数,则an的前2n项和为?已知数列｛an｝中,an=｛2^[(n-1)/2] n为奇数, 2^(-n/2) n为偶数,则an的前2n项和为?](/uploads/image/z/8822129-41-9.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E4%B8%AD%2Can%3D2%5E%5B%28n-1%29%2F2%5Dn%E4%B8%BA%E5%A5%87%E6%95%B0%2Can%3D2%5E%28-n%2F2%29n%E4%B8%BA%E5%81%B6%E6%95%B0%2C%E5%88%99an%E7%9A%84%E5%89%8D2n%E9%A1%B9%E5%92%8C%E4%B8%BA%3F%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E4%B8%AD%2Can%3D%EF%BD%9B2%5E%5B%28n-1%29%2F2%5D%E3%80%80n%E4%B8%BA%E5%A5%87%E6%95%B0%2C%E3%80%80%E3%80%80%E3%80%80%E3%80%80%E3%80%80%E3%80%80%E3%80%80%E3%80%80%E3%80%80%E3%80%80%E3%80%802%5E%28-n%2F2%29%E3%80%80%E3%80%80+n%E4%B8%BA%E5%81%B6%E6%95%B0%2C%E5%88%99an%E7%9A%84%E5%89%8D2n%E9%A1%B9%E5%92%8C%E4%B8%BA%3F)
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已知数列｛an｝中,an=2^[(n-1)/2]n为奇数,an=2^(-n/2)n为偶数,则an的前2n项和为?已知数列｛an｝中,an=｛2^[(n-1)/2] n为奇数, 2^(-n/2) n为偶数,则an的前2n项和为?
已知数列｛an｝中,an=2^[(n-1)/2]n为奇数,an=2^(-n/2)n为偶数,则an的前2n项和为?
已知数列｛an｝中,an=｛2^[(n-1)/2] n为奇数,
2^(-n/2) n为偶数,
则an的前2n项和为?
已知数列｛an｝中,an=2^[(n-1)/2]n为奇数,an=2^(-n/2)n为偶数,则an的前2n项和为?已知数列｛an｝中,an=｛2^[(n-1)/2] n为奇数, 2^(-n/2) n为偶数,则an的前2n项和为?
答：
{an}前2n项中有n个奇数项和n个偶数项,设奇数项构成数列{bn},偶数项构成数列{cn}
则b1=a1=1,{bn}公比为a3/a1=2,所以bn=2^(n-1)
c1=a2=1/2,{cn}公比为a4/a2=1/2,所以cn=1/2^n
记{bn}前n项和为Tn,{cn}前n项和为Un,则：
S2n=Tn+Un
=1×(1-2^n)/(1-2)+1/2×(1-1/2^n)/(1-1/2)
=2^n-1+1-1/2^n
=2^n-1/2^n