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Binomial Theorem question

2024 · 4 Apr · Shift 1 · Q60

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PYQ Library
JEE Main
Mathematics
Binomial Theorem
2024 · 4 Apr · Shift 1 · Q60

Binomial Theorem question

2024 · 4 Apr · Shift 1 · Q60

JEE MainMathematicsBinomial TheoremNumerical+4 / −1

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

\underline{\hspace{2cm}}

.

Numerical answer

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