Question

高一数学作业求解析

Answer 1

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Answer 2

a(n+1) = 3a(n) + 3^(n+1) ...... (1)

a1 = 1
a2 = 3*a1 + 9 = 12
a3 = 3*a2 + 27 = 63

(1) 两边同除以 3^(n+1)
a(n+1)/3^(n+1) =a(n)/3^n + 1
令 b(n) = a(n)/3^n
b(n+1) = b(n) + 1
b1 = a1/3 = 1/3
b(n) = n - 2/3
s(n) = n^2/2 - n/6

Answer 3

A(n+1)-3An为等比数列可得A(n+1)-3An=3的n+1次方

1. a2-3a1=9  a2=12

2. 
   

a3-3a2=3*9   a3=36

2.

A(n+1)-3An=3的n+1次方   两边同时除以3的n+1次方得

A(n+1)/3的n+1次方 - An/3的n次方=1

设Bn=An/3的n次方

则Bn为等差数列=1/3+1*（n-1）=n-2/3

求和1/2*（1/3+n-2/3）*n=n*(3n-1)/6