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Solution of a recurrence relation

$Version (* "13.1.0 for Mac OS X x86 (64-bit) (June 16, 2022)" *) WolframAlpha["step-by-step solve a[n+1]==(1+α) a[n]+γ"]
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Solution of a recurrence relation

I think CASes apply a usual method of solving linear recurrence relations with constant coefficients (for example, see Wiki for info). In any case the result of the command of Maple ...
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2 votes

Solution of a recurrence relation

Clear[a, \[Alpha], n] RSolve[a[n + 1] == (1 + α) a[n] + γ, a[n], n] $$\left\{\left\{a(n)\to -\frac{\gamma \left(1-(\alpha +1)^n\right)}{\alpha }+c_1 (\alpha +1)^{...
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