cn=2/3(4n-2)*(1/3)^(n-1),求证:当n≥2时,数列是递减数列

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cn=2/3(4n-2)*(1/3)^(n-1),求证:当n≥2时,数列是递减数列

cn=2/3(4n-2)*(1/3)^(n-1),求证:当n≥2时,数列是递减数列
cn=2/3(4n-2)*(1/3)^(n-1),求证:当n≥2时,数列是递减数列

cn=2/3(4n-2)*(1/3)^(n-1),求证:当n≥2时,数列是递减数列
做一下商就好:

consider
f(x) = (2/3)(4x-2)(1/3)^(x-1)
f'(x) = (2/3)( 4(1/3)^(x-1) - (ln3)(4x-2)(1/3)^(x-1) )
= (2/3) (1/3)^(x-1) . ( 4+2ln3 - 4xln3 )
f'(x) <0
6+2ln3 - 4xln3 <0
x > (6+2ln3)/(4ln3) =1.41
choose n =2
ie
n≥2
cn = (2/3)(4n-2)(1/3)^(n-1)是递减数列