如果数列{an}是等差数列,设bn=(1/2)^an,数列{bn}是等比数列吗?
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如果数列{an}是等差数列,设bn=(1/2)^an,数列{bn}是等比数列吗?如果数列{an}是等差数列,设bn=(1/2)^an,数列{bn}是等比数列吗?如果数列{an}是等差数列,设bn=(1
如果数列{an}是等差数列,设bn=(1/2)^an,数列{bn}是等比数列吗?
如果数列{an}是等差数列,设bn=(1/2)^an,数列{bn}是等比数列吗?
如果数列{an}是等差数列,设bn=(1/2)^an,数列{bn}是等比数列吗?
数列{an}是等差数列,设公差为d,
则an-a(n-1)=d(常数)
bn=(1/2)^an,
则bn/b(n-1)=[ (1/2)^an]/[ (1/2)^a(n-1)]
=(1/2)^(an- a(n-1))= (1/2)^d
因为d是常数,所以(1/2)^d是常数,
∴数列{bn}是等比数列.
是 简单假设一个特殊情况就能推导出来
不妨设an=a1+nd.
因为bn=(1/2)^an
所以bn+1=(1/2)^an+1
bn==(1/2)^an
所以(bn+1)/ bn = (1/2)^an+1)/ (1/2)^an = (1/2)^an+1-an==(1/2)^(a1+nd+d-a1-nd)
=(1/2)^d
因为d是常数
故数列{bn}为等比数列
如果数列{an}是等差数列,设bn=(1/2)^an,数列{bn}是等比数列吗?
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