an=(2n-1)*2^(n-1),求Sn
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an=(2n-1)*2^(n-1),求Sn
an=(2n-1)*2^(n-1),求Sn
an=(2n-1)*2^(n-1),求Sn
Sn=1+3*2+5*2^2+.+(2n-1)*2^(n-1)
2Sn=1*2+3*2^2+5*2^3+.+(2n-1)*2^n
Sn-2Sn=1+2[2+2^2+.+2^(n-1)]-(2n-1)*2^n
-Sn=1+2[2^(n-1)-1]/(2-1)-(2n-1)*2^n
Sn=-1-2^n+2+(2n-1)*2^n
=(2n-2)*2^n+1
Sn=1 + 3*2 + 5*2^2 +......+(2n-1)*2^(n-1) --->(1)
2Sn= 1*2 + 3*2^2+.......+(2n-3)*2^(n-1)+(2n-1)*2^n ------>(2)
(2)-(1) 得到
Sn=(2n-1)*2^n-[2^2+2^3+....+2^n]-1
=(2n-3)*2^n+3
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