x^n এর সহগ নির্ণয় বিষয়ক
(r+1)r!2r! \frac{(\mathrm{r}+1) \mathrm{r} !}{2 \mathrm{r} !} 2r!(r+1)r!
(r+1) (r+1) (r+1)
1
0
(1+2x+3x2+…)12={(1−x)−2}12=(1−x)−1=1+x+x2+…xr+…∞∴xr \left(1+2 \mathrm{x}+3 \mathrm{x}^{2}+\ldots\right)^{\frac{1}{2}} \\= \left\{(1-\mathrm{x})^{-2}\right\}^{\frac{1}{2}}=(1-\mathrm{x})^{-1}=1+\mathrm{x}+\mathrm{x}^{2}+\ldots \mathrm{x}^{\mathrm{r}}+\ldots \infty \quad \therefore \mathrm{x}^{\mathrm{r}} (1+2x+3x2+…)21={(1−x)−2}21=(1−x)−1=1+x+x2+…xr+…∞∴xr এর সহগ 1
(a+x)n\left(a+x\right)^n(a+x)nএর বিস্তৃতির r-তম পদ হল-
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 :
The value of C12+C22....+Cn2C_1 ^2+C_2 ^2....+C_n ^2C12+C22....+Cn2 (where CiC_iCi is the ithi^{th}ith coefficient of (1+x)n(1+x)^n(1+x)n expansion), is:
