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Mathematical Induction and Binomial Theorem question

2016 · Shift 1 · Q29

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JEE Advanced
Mathematics
Mathematical Induction and Binomial Theorem
2016 · Shift 1 · Q29

Mathematical Induction and Binomial Theorem question

2016 · Shift 1 · Q29

JEE AdvancedMathematicsMathematical Induction and Binomial TheoremNumerical+3 / −1

Let

m

be the smallest positive integer such that the coefficient of

{x^2}

in the expansion of

{\left( {1 + x} \right)^2} + {\left( {1 + x} \right)^3} + ........ + {\left( {1 + x} \right)^{49}} + {\left( {1 + mx} \right)^{50}}\,\,

is

\left( {3n + 1} \right)\,{}^{51}{C_3}

for some positive integer

n

. Then the value of

n

is

Numerical answer

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