Let a=1+(² C₂)/(3 !)+(³ C₂)/(4 !)+(⁴ C₂)/(5 !)+...., b=1+(¹ C₀+ ¹ C₁)/(1 !)+(² C₀+ ² C₁+ ² C₂)/(2 !)+(³ C₀+ ³ C₁+ ³ C₂+ ³ C₃)/(3 !)+.... Then (2 b)/(a²) is equal to _ _ _ _ _.

Binomial Theorem and Its Simple Applications: JEE Main 2024 Mathematics question

JEE Main 2024 · 4 Apr, Morning shift · Q28

JEE Main 20244 Apr, Morning shiftMathematicsHardBinomial Theorem and Its Simple Applications131× since 2002

Let

a=1+\frac{{ }^2 \mathrm{C}_2}{3 !}+\frac{{ }^3 \mathrm{C}_2}{4 !}+\frac{{ }^4 \mathrm{C}_2}{5 !}+...., \mathrm{b}=1+\frac{{ }^1 \mathrm{C}_0+{ }^1 \mathrm{C}_1}{1 !}+\frac{{ }^2 \mathrm{C}_0+{ }^2 \mathrm{C}_1+{ }^2 \mathrm{C}_2}{2 !}+\frac{{ }^3 \mathrm{C}_0+{ }^3 \mathrm{C}_1+{ }^3 \mathrm{C}_2+{ }^3 \mathrm{C}_3}{3 !}+....

Then

\frac{2 b}{a^2}

is equal to _________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2024 · 4 Apr, Morning shift · Q28

JEE Main 20244 Apr, Morning shiftMathematicsHardBinomial Theorem and Its Simple Applications131× since 2002

Let

a=1+\frac{{ }^2 \mathrm{C}_2}{3 !}+\frac{{ }^3 \mathrm{C}_2}{4 !}+\frac{{ }^4 \mathrm{C}_2}{5 !}+...., \mathrm{b}=1+\frac{{ }^1 \mathrm{C}_0+{ }^1 \mathrm{C}_1}{1 !}+\frac{{ }^2 \mathrm{C}_0+{ }^2 \mathrm{C}_1+{ }^2 \mathrm{C}_2}{2 !}+\frac{{ }^3 \mathrm{C}_0+{ }^3 \mathrm{C}_1+{ }^3 \mathrm{C}_2+{ }^3 \mathrm{C}_3}{3 !}+....

Then

\frac{2 b}{a^2}

is equal to _________.

Your answerType your answer. Integers and decimals are accepted.