若数列{an}满足:a1=1,an+1=2an,n=1,2,3….则a1+a2+…+an=______.
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![若数列{an}满足:a1=1,an+1=2an,n=1,2,3….则a1+a2+…+an=______.](/uploads/image/z/11522843-35-3.jpg?t=%E8%8B%A5%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E6%BB%A1%E8%B6%B3%EF%BC%9Aa1%3D1%2Can%2B1%3D2an%2Cn%3D1%2C2%2C3%E2%80%A6.%E5%88%99a1%2Ba2%2B%E2%80%A6%2Ban%3D______.)
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若数列{an}满足:a1=1,an+1=2an,n=1,2,3….则a1+a2+…+an=______.
若数列{an}满足:a1=1,an+1=2an,n=1,2,3….则a1+a2+…+an=______.
若数列{an}满足:a1=1,an+1=2an,n=1,2,3….则a1+a2+…+an=______.
因为an+1=2an,所以an+1/an=2
所以数列{an}为首项为1公比为2的等比数列
所以 a1+a2+…+an=2^n-1
a1=1;
an+1=2an.可得:an=1
a1+a2+…+an=n;
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