Hello ,would you please solve the following non homogenous recursion:
[{a[n+1]-a[n]=2n+3,a[0]=1},a,n]
Hello, seamoh!
We have: .Solve the following non-homogenous recursion:
. .
The sequences seems to be squares.
. . I would conjecture that: .
Subtract [1] from [2]: .
Subtract [3] from [4]: .
We have: .
Let
Divide by
We have a triple root: .
The function has the form: .
. . That is: .
We know the first three terms:
. .
Solve the system: . . . . Hence: .
. . Therefore: .
Hello, seamoh!
We have: .Solve the following non-homogenous recursion:
. .
The sequences seems to be squares.
. . I would conjecture that: . n+1)^2" alt="a(n) \:=\n+1)^2" />
Subtract [1] from [2]: .
Subtract [3] from [4]: .
We have: .
Let
Divide by
We have a triple root: .
The function has the form: .
. . That is: .
We know the first three terms:
. .
Solve the system: . . . . Hence: .
. . Therefore: .