IGNOU BMTC 103 2026 - यदि पुनरावृत्ति संबंध का हल है , तो &

Question

यदि पुनरावृत्ति संबंध $u_n + \alpha u_{n-1} + \beta u_{n-2} = f(n), (n \ge 2)$ का हल $u_n = 1 - 2n + 3 \cdot 2^n$ है , तो $\alpha, \beta$ और f(n) के मान ज्ञात कीजिए।

20 Jan 2026

Answer :

Word Count : 183

दिया है पुनरावृत्ति संबंध uₙ + αuₙ₋₁ + βuₙ₋₂ = f(n), (n ≥ 2) और इसका हल uₙ = 1 − 2n + 3·2ⁿ अब uₙ₋₁ = 1 − 2(n−1) + 3·2ⁿ⁻¹ = 3 − 2n + (3/2)·2ⁿ uₙ₋₂ = 1 − 2(n−2) + 3·2ⁿ⁻² = 5 − 2n

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