Question

If P =$\lim_{n \rightarrow \infty}$ (ea².e³a⁴…..e^n–1aⁿ)$1/(n^{2} + 1)$, then P⁴ equals

• A. ea²
• B. e²a²
• C. ea
• D. e²a

Answer 1

Answer: (C)

ea

Answer 2

P = $\lim _ { n \rightarrow \infty }$ (e^{1+3+…..n/2 terms} a^{2+4+…..n/2 terms})

= $\lim _ { n \rightarrow \infty }$ (e^{n/4 (1+ n–1)} a^{n/4(2 + n)}) $1 / \left( n ^ { 2 } + 1 \right)$

= $\lim _ { n \rightarrow \infty }$ $e ^ { \frac { n ^ { 2 } } { 4 \left( n ^ { 2 } + 1 \right) } } a ^ { \frac { 2 n + n ^ { 2 } } { 4 \left( n ^ { 2 } + 1 \right) } }$ = e^1/4 . a^1/4 ⇒ P⁴ = e.a