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Sequences and Series question

2024 · 8 Apr · Shift 1 · Q57

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JEE Main
Mathematics
Sequences and Series
2024 · 8 Apr · Shift 1 · Q57

Sequences and Series question

2024 · 8 Apr · Shift 1 · Q57

JEE MainMathematicsSequences and SeriesNumerical+4 / −1

Let

\alpha=\sum_{r=0}^n\left(4 r^2+2 r+1\right){ }^n C_r

and

\beta=\left(\sum_{r=0}^n \frac{{ }^n C_r}{r+1}\right)+\frac{1}{n+1}

. If

140\lt \frac{2 \alpha}{\beta}\lt 281

, then the value of

n

is

\underline{\hspace{2cm}}

.

Numerical answer

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