adam rainer

1.1.1. 20238AIChatGPTchatbot.
200B AI AI.
260410 API .
ChatGPT 2.0 ProGemini 3.1 ProGeminiSTEMGPT.
Seed-2.0 2 14 2.0 App.
AIAIAIflow.
AI .
k' = k \beta = 1/2 Seed AI .
1 2AI.
ChatGTPAIAI.

1.1.1. 20238AIChatGPTchatbot.
200B AI AI.
260410 API .
ChatGPT 2.0 ProGemini 3.1 ProGeminiSTEMGPT.
Seed-2.0 2 14 2.0 App.
AIAIAIflow.
AI .
k' = k \beta = 1/2 Seed AI .
1 2AI.
ChatGTPAIAI.
To find the explicit formula, we first solve the homogeneous part of the recurrence relation \( a_n = 2a_{n-1} \), which gives \( a_n = C \cdot 2^n \) for some constant \( C \). Next, we find a particular solution for the non-homogeneous recurrence. Trying a constant solution \( a_n = A \):
A = 2A - 3 \im
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