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The coefficient of \({x^{100}}\) in the expansion of \(\sum\limits_{j = 0}^{200} {{{\left( {1 + x} \right)}^j}} \) is
i.e.
Coefficient of in the above expansion is .
If in the expansion of \({\left( {1 + x} \right)^{21}}\), the coefficient of \({x^r}\) and \({x^{r + 1}}\) be equal, then r is
i.e.
If\(\left x \right < \frac{1}{2}\), then the coefficient of \({x^r}\) in the expansion of \(\dfrac{{\left( {1 + 2x} \right)}}{{{{\left( {1 – 2x} \right)}^2}}}\) is
Coefficient of is
The term independent of x in the expansion of \({\left( {\frac{{2\sqrt x }}{5} – \frac{1}{{2x\sqrt x }}} \right)^{11}}\) is
r can’t be rational.
There are no term independent of x.
The sum of coefficients in the expansion of \({\left( {\dfrac{1}{x} + 2x} \right)^n}\) is 6561, then coefficient of the term independent of x is
; the sum of coefficients of the
expansion is 6561.
i.e.
Coefficient of term independent of
x is
If the coefficients of \({x^{ – 2}}\) and \({x^{ – 4}}\) in the expansion of \({\left( {{x^{1/3}} + \frac{1}{{2{x^{1/3}}}}} \right)^{18}},\left( {x > 0} \right)\) are m and n respectively, then \(\frac{m}{n}\) is equal to
The sum of coefficient of integral powers of x in the expansion of \({\left( {1 – 2\sqrt x } \right)^{50}} + {\left( {1 + 2x} \right)^{50}}\)
set x=1 to obtain
(Sum of coefficients of integral power of x)
Sum of cofficients of integral
power of x
If the coefficients of the 3consecutive terms in the expansion of \({(1 + x)^n}\) are in the ratio 1:7:42, then the first of these terms in the expansion is
If the coefficients of \({x^3}\& {x^4}\) in the expansion of \((1 + ax + b{x^2}){(1 – 2x)^{18}}\) in powers of x are both zero, then (a,b) is equal to
The coefficient of is
The coefficient of is
3b32a=240(ii)
solving (i) and (ii) we get
The coefficient of the \({5^{ \text {th}}}\) term in the expansion of \({\left( {5{x^2} – \frac{1}{{2x}}} \right)^8}\) is
coefficient of this term is
Find the coefficient of \( x^{8}\) in expansion of \({\left( {{x^4} – \frac{1}{{3{x^2}}}} \right)^7}\).
coefficient of
Coefficient of \( x^{7}\) in the expansion of \({\left( {1 + 3x + 3{x^2} + {x^3}} \right)^4}\) is
Coefficient of is .
If \({S_n} = \sum\limits_{r = 0}^n {\frac{1}{{{}^n{C_r}}}} \) and \({t_n} = \sum\limits_{r = 0}^n {\frac{r}{{{}^n{C_r}}}} \), then \(\frac{{{t_n}}}{{{S_n}}}\) is equal to
The number of integral terms in the expansion of \({\left( {\sqrt 3 + \sqrt[8]{5}} \right)^{256}}\) is
For integral terms are both positive integers.