x^n এর সহগ নির্ণয় বিষয়ক
(1+x1−x) \left ( \frac{1 + x}{1 - x} \right ) (1−x1+x) এর বিস্তৃতিতে x² এর সহগ কত?
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1+x1−x=(1+x)(1−x)−1=(1+x)(1+x+x2+x3+…)=(1+x+x2+…..)+(x+x2+x3+…)∴x2 এর সহগ=1+1=2 \begin{aligned} \text { } \frac{1+x}{1-x} & =(1+x)(1-x)^{-1} \\ & =(1+x)\left(1+x+x^{2}+x^{3}+\ldots\right) \\ & =\left(1+x+x^{2}+\ldots . .\right)+\left(x+x^{2}+x^{3}+\ldots\right) \\ \therefore x^{2} \text { এর সহগ} & =1+1=2\end{aligned} 1−x1+x∴x2 এর সহগ=(1+x)(1−x)−1=(1+x)(1+x+x2+x3+…)=(1+x+x2+…..)+(x+x2+x3+…)=1+1=2
The coefficient of x3 x^3 x3 in the expansion of (1+2x)6(1−x)7 (1+2x)^6(1-x)^7 (1+2x)6(1−x)7 is
The coefficient of x2x^2x2 in expansion of the product(2-x2x^2x2).((1+2x+3x2)6(1 + 2x + 3x^2)^6(1+2x+3x2)6 + (1−14x2)6(1-1 4x^2)^6(1−14x2)6) is :
If xm{ x }^{ m }xm occurs in the expansion of (x+1x2)2n(x+\frac { 1 }{ { x }^{ 2 } } )^{ 2n }(x+x21)2n, the coefficient of xm{ x }^{ m }xm, is
The sum of the coefficients in the expansion of (1+5x−7x3)3165{\left( {1 + 5x - 7{x^3}} \right)^{3165}}(1+5x−7x3)3165 is
