x^n এর সহগ নির্ণয় বিষয়ক
1(1−x)(3−x) \frac{1}{\left ( 1 - x \right ) \left ( 3 - x \right )} (1−x)(3−x)1
এর বৃস্তৃতিতে x10 এর সহগ হবে-
1(1−x)(3−x)=13(1−x)(1−x3)=13[1(1−x)(1−x3)] \frac{1}{(1-x)(3-x)}=\frac{1}{3(1-x)\left(1-\frac{x}{3}\right)}=\frac{1}{3}\left[\frac{1}{(1-x)\left(1-\frac{x}{3}\right)}\right] (1−x)(3−x)1=3(1−x)(1−3x)1=31[(1−x)(1−3x)1]
সূত্র: xr(1−ax)(1−bx)=an−r+1−bn−r+1a−b \frac{x^{r}}{(1-a x)(1-b x)}=\frac{a^{n-r+1}-b^{n-r+1}}{a-b} (1−ax)(1−bx)xr=a−ban−r+1−bn−r+1
∴13×[(1)10−0+1−(1/3)10−0+11−13]=13×32[1−3−11]=12[1−3−11] \therefore \frac{1}{3} \times\left[\frac{(1)^{10-0+1}-(1 / 3)^{10-0+1}}{1-\frac{1}{3}}\right]=\frac{1}{3} \times \frac{3}{2}\left[1-3^{-11}\right]=\frac{1}{2}\left[1-3^{-11}\right] ∴31×[1−31(1)10−0+1−(1/3)10−0+1]=31×23[1−3−11]=21[1−3−11]
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:
(1+x)21+(1+x)22+..+(1+x)30(1+x)^{21}+(1+x)^{22}+..+(1+x)^{30}(1+x)21+(1+x)22+..+(1+x)30 in the expansion of this what is the coefficient of x5x^{5}x5 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
