Find the number of terms in the expansion of x 1- x 2- x 3- x k nA- n-k Ck-1B- n Ck- n-k-1 CnD- n-k-1 Ck

The correct option is C (x_1+x_2+x_3......x_k)^n=∑_r_1+r_2+r_3...r_k=nn!/r_1!+r_2!× ...r_k!× x_1^r_1x_2^r_2....x_k^rk Total numbers of terms in this expansion ...

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Byju's Answer

Standard XI

Mathematics

Middle Terms

Find the numb...

Question

Find the number of terms in the expansion of $(x_{1} + x_{2} + x_{3} . . . . x_{k})^{n}$

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Solution

The correct option is C

$(x_{1} + x_{2} + x_{3} . . . . . . x_{k})^{n} = \sum_{r_{1} + r_{2} + r_{3} . . . r_{k}} = n \frac{n!}{r_{1}! + r_{2}! \times . . . r_{k}!} \times x_{1}^{r_{1}} x_{2}^{r_{2}} . . . . x_{k}^{r k}$
Total numbers of terms in this expansion in this expansion is equal to the number of non-negative solution of $r_{1} + r_{2} + . . . r_{k} = n$
= $^{n + k - 1} C_{k - 1}$
= $^{n + k - 1} C_{n}$

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ϵ

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Find the number of terms in the expansion of (x1+x2+x3....xk)n

The correct option is C (x1+x2+x3......xk)n=∑r1+r2+r3...rk=nn!r1!+r2!×...rk!×xr11xr22....xrkk Total numbers of terms in this expansion in this expansion is equal to the number of non-negative solution of r1+r2+...rk=n =n+k−1Ck−1 =n+k−1Cn

Find the number of terms in the expansion of $(x_{1} + x_{2} + x_{3} . . . . x_{k})^{n}$