an=2*3^n-1 若数列bn满足bn=an+(-1)^n*ln(an),求数列bn前n项和Sn

问题描述:

an=2*3^n-1 若数列bn满足bn=an+(-1)^n*ln(an),求数列bn前n项和Sn

an=2*3^(n-1)
bn = an+ (-1)^n*ln(an)
= 2*3^(n-1) + (-1)^n* [ ln2 + (n-1)ln3 ]
Sn = b1+b2+..+bn
= (3^n-1) + (-1)^n*[ nln2 + (n(n-1)/2)ln3 ]