Binomial Theorem
Series Summation via Exponential
nta_pyq_2024_apr
Grade 11
Question:
Let $a=1+\dfrac{^2C_2}{3!}+\dfrac{^3C_2}{4!}+\dfrac{^4C_2}{5!}+\cdots$ and $b=1+\dfrac{^1C_0+^1C_1}{1!}+\dfrac{^2C_0+^2C_1+^2C_2}{2!}+\dfrac{^3C_0+^3C_1+^3C_2+^3C_3}{3!}+\cdots$. Then $\dfrac{2b}{a^2}$ is equal to:
Step-by-Step Solution
Key Concept: $a=e/2$, $b=e^2$. $2b/a^2=2e^2/(e^2/4)=8$.
$2b/a^2=8$.
Correct Answer: 8