Question

Find positive value of n for which the coefficient of x2 in the expansion of ( 1 + x )n

is 10.​

Answer 1

SOLUTION

TO DETERMINE

The positive value of n for which the coefficient of x² in the expansion of

$\sf{ {(1 + x)}^{n} \: \: is \: \: 10 }$

EVALUATION

$\sf{First \: we \: take \: a \: look \: on \: the \: expansion \: of \: \: {(1 + x)}^{n} }$

$\sf{ {(1 + x)}^{n} = {}^{n}C_0 + {}^{n}C_1 \: x + {}^{n}C_2 \: {x}^{2} + {}^{n}C_3 \: {x}^{3} + ... + {}^{n}C_n \: {x}^{n} }$

$\sf{Coefficient \: of \: \: {x}^{2} \: \: in \: {(1 + x)}^{n} \: \: is \: \: {}^{n} C_2 }$

So by the given condition

$\sf{ {}^{n} C_2 = 10 }$

$\sf{ \implies \: {}^{n} C_2 = {}^{5} C_2 }$

$\sf{ \implies \: n = 5 }$

FINAL ANSWER

The required value of n = 5

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Answer 2

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