Subtopic: Thermodynamic principles of I.C. engines
Question Statement:
The series represented by aₙ = (n²−2n)/(3n²+n) is
Options:
(A) convergent
(B) divergent
(C) asymptotic
(D) oscillatory
Official Answer Key:
A
Step-by-Step Solution & Explanation
Divide numerator and denominator by n²: aₙ = (1 − 2/n)/(3 + 1/n). As n → ∞, the terms 2/n and 1/n → 0, so lim(n→∞) aₙ = 1/3, a finite value. Since the sequence approaches a finite limit, the series/sequence is convergent. ‘Divergent’ (B) would require the limit to be infinite or non-existent; ‘asymptotic’ (C) and ‘oscillatory’ (D) do not describe a monotonically-approaching rational sequence of this form. Hence (A) is correct.
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