TS EAMCET · Maths · Sequences and Series
The value of the greatest integer \(k\) satisfying the inequation \(2^{n+4}+12 \geq k(n+4)\) for all \(n \in \mathrm{~N}\) is
- A 7
- B 8
- C 9
- D 10
Answer & Solution
Correct Answer
(B) 8
Step-by-step Solution
Detailed explanation
Let \(x = n+4\). For all \(n \in \mathrm{N}\), \(x \in \{5, 6, 7, \ldots\}\). The inequation is \(k \leq \frac{2^x+12}{x}\). For \(x=5\): \(k \leq \frac{2^5+12}{5} = \frac{32+12}{5} = \frac{44}{5} = 8.8\). For \(x=6\):…
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