等差数列求通项公式的题,请问这怎么转化的呢?
Sn=2/3(4^n-1)
S(n-1)=2/3[4^(n-1)-1]
Sn-S(n-1)
=2/3(4^n-1)-2/3[4^(n-1)-1]
=2/3*[4^n-1-4^(n-1)+1]
=2/3*[4^n-4^(n-1)]
=2/3*[4*4^(n-1)-4^(n-1)]
=2/3*4^(n-1)*(4-1)
=2/3*2^2(n-1)*3
=2*2^(2n-2)
=2^(1+2n-2)
=2^(2n-1)
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Sn=2/3(4^n-1)
S(n-1)=2/3[4^(n-1)-1]
Sn-S(n-1)
=2/3(4^n-1)-2/3[4^(n-1)-1]
=2/3*[4^n-1-4^(n-1)+1]
=2/3*[4^n-4^(n-1)]
=2/3*[4*4^(n-1)-4^(n-1)]
=2/3*4^(n-1)*(4-1)
=2/3*2^2(n-1)*3
=2*2^(2n-2)
=2^(1+2n-2)
=2^(2n-1)