求数列2+a,5+a²,8+a³,.(3n-1)+a^n的前几项和求详细解答过程谢谢
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![求数列2+a,5+a²,8+a³,.(3n-1)+a^n的前几项和求详细解答过程谢谢](/uploads/image/z/1092303-63-3.jpg?t=%E6%B1%82%E6%95%B0%E5%88%972%2Ba%2C5%2Ba%26%23178%3B%2C8%2Ba%26%23179%3B%2C.%EF%BC%883n-1%EF%BC%89%2Ba%5En%E7%9A%84%E5%89%8D%E5%87%A0%E9%A1%B9%E5%92%8C%E6%B1%82%E8%AF%A6%E7%BB%86%E8%A7%A3%E7%AD%94%E8%BF%87%E7%A8%8B%E8%B0%A2%E8%B0%A2)
求数列2+a,5+a²,8+a³,.(3n-1)+a^n的前几项和求详细解答过程谢谢
求数列2+a,5+a²,8+a³,.(3n-1)+a^n的前几项和
求详细解答过程谢谢
求数列2+a,5+a²,8+a³,.(3n-1)+a^n的前几项和求详细解答过程谢谢
let
S = 1.a^1+2.a^2+.+n.a^n (1)
aS = 1.a^2+2.a^3+.+n.a^(n+1) (2)
(2)-(1)
(a-1)S = n.a^(n+1) - ( a+a^2+...+a^n)
= n.a^(n+1) - a( a^n-1)/(a-1)
S = [1/(a-1)][n.a^(n+1) - a( a^n-1)/(a-1)]
bn= 3n-1
cn = a^n
dn=bn + cn
= (3n-1) .a^n
= 3( n.a^n) - a^n
Sn =d1+d2+...+dn
= 3S - a(a^n-1)/(a-1)
=[3/(a-1)][n.a^(n+1) - a( a^n-1)/(a-1)] - a(a^n-1)/(a-1)
数列2+a,5+a²,8+a³,.(3n-1)+a^n的前几项和
= Sn
=[3/(a-1)][n.a^(n+1) - a( a^n-1)/(a-1)] - a(a^n-1)/(a-1)