Question

已知数列{an}中,an等于3的n+1次方分之2n-3

Answer 1

an=(2n-3)/3^(n+1)
sn=-1/3^2+1/3^3+3/3^4+.+(2n-3)/3^(n+1)
sn/3=-1/3^3+1/3^4+3/3^5+.+(2n-5)/3^(n+1)+(2n-3)/3^(n+2)
sn-sn/3=-1/3^2+2/3^3+2/3^4+.+2/3^(n+1)-(2n-3)/3^(n+2)
2sn/3=-1/3^2+2/3^2*[1-(1/3)^(n-1)]/(1-1/3)-(2n-3)/3^(n+2)
2sn/3=-1/3^2+1/3*[1-(1/3)^(n-1)]-(2n-3)/3^(n+2)
2sn=-1/3+1-(1/3)^(n-1)-(2n-3)/3^(n+1)
2sn=2/3-9*1/3^(n+1)-(2n-3)/3^(n+1)
2sn=2/3-(9+2n-3)/3^(n+1)
2sn=2/3-(2n+6)/3^(n+1)
sn=1/3-(n+3)/3^(n+1)