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7.Binomial Theorem
normal
${\left( {1 + x} \right)^n}{\left( {1 + \frac{1}{x}} \right)^n}$ ના વિસ્તરણમાં $\frac{1}{x}$ નો સહગુણક મેળવો
A
$\frac{{n!}}{{(n - 1)!\left( {n + 1} \right)!}}$
B
$\frac{{2n!}}{{(n - 1)!\left( {n + 1} \right)!}}$
C
$\frac{{(2n)!}}{{(2n - 1)!\left( {2n + 1} \right)!}}$
D
એક પણ નહી
Solution
Simplifying, we get $\frac{(1+x)^{2 n}}{x^{n}} \ldots( i )$
$T_{r+1}={ }^{2 n} C_{r} x^{r-n}$
Hence coefficient of $x^{-1}$
$=2 n C_{n-1}$
$=\frac{(2 n) !}{(n-1) !(n+1) !}$
Standard 11
Mathematics
