数列分组求和

Sn=(3^2-2^2)/(3-2)+(3^3-2^3)/(3-2)+…+[3^(n+1)-2^(n+1)]/(3-2)…①
=(3^2-2^2)+(3^3-2^3)+…+[3^(n+1)-2^(n+1)]
=[3^2+3^3+…+3^(n+1)]-[2^2+2^3+…+2^(n+1)]
=(3^n-1)*3^2/(3-1)-(2^n-1)*2^2/(2-1)…②
=1/2*[3^(n+2)-3^2]-[2^(n+2)-2^2]
=1/2*[3^(n+2)-9]-1/2*2*[2^(n+2)-4]
=1/2*{3^(n+2)-9-2*[2^(n+2)-4]}
=1/2*[3^(n+2)-2^(n+3)-1]
附公式
①x^n-y^n=(x-y)[x^(n-1)+x^(n-2)*y+x^(n-3)*y^2+…+x*y^(n-2)+y^(n-1)]（n为正整数）
变形得此步所用的x^(n-1)+x^(n-2)*y+x^(n-3)*y^2+…+x*y^(n-2)+y^(n-1)=(x^n-y^n)/(x-y)
②等比数列求和公式：(q^n-1)a1/(q-1)
其中q为公比,n为项数,a1为首项