(n(n+1))/2+(0.5（1-0.5^n))/0.5最后化解为?等比数列前N项Sn=2^n+a,a=?谢谢了,大神帮忙啊

Question

(n(n+1))/2+(0.5（1-0.5^n))/0.5 最后化解为?等比数列前N项Sn=2^n+a,a=?谢谢了,大神帮忙啊

Answer 1

(n(n+1))/2+(0.5（1-0.5^n))/0.5 =2[n(n+1))/2+(0.5（1-0.5^n)] =n(n+1)+1-0.5^n =n^2+ n + 1- 1/2^n an为比数列,Sn=2^n+a S1=a1=2+a,n≥2时,Sn-Sn-1=an=2^n-2^(n-1)=2^(n-1),所以2+a=2^(n-1),a=2^(n-1)-2....