数列3/2,9/4,25/8,65/16.求前n项和Sn.

数列3/2,9/4,25/8,65/16.求前n项和Sn.
数列3/2,9/4,25/8,65/16.求前n项和Sn.

数列3/2,9/4,25/8,65/16.求前n项和Sn.
a(n)=(3/2)^n
S(n)=a(1)*[1-(3/2)^n]/(1-3/2)=3*[(3/2)^n-1]

an=((2^n)*n+1)/(2^n)=n+1/(2^n)
sn=(1+1/2)+(2+1/4)+(3+1/8)+······+（n+1/(2^n))=(1+2+3+······+n)+(1/2+1/4+1/8+·····+1/(2^n)）=n*（n+1)/2+(1-1/(2^n))

二楼正解！

an=((2^n)*n+1)/(2^n)=n+1/(2^n)
Sn=n*（n+1)/2+(1-1/(2^n))