Question

Find positive value of n for which the coefficient of x² in the expansion of ( 1 + x)^n is 10.​

Answer 1

Answer:

SOLUTION

TO DETERMINE

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

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

n

is10

EVALUATION

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

n

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

2

in(1+x)

n

is

n

C

2

So by the given condition

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

n

C

2

=10

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

n

C

2

=

5

C

2

\sf{ \implies \: n = 5 }⟹n=5

FINAL ANSWER

The required value of n = 5