The sum of all rational terms in the expansio | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The general term in the expansion of $(2+\sqrt{3})^8$ is given by $T_{r+1} = { }^8 C_r (2)^{8-r} (\sqrt{3})^r$. For the term to be rational,$r$ mu

Vedclass · Accepted Answer

$18817$

Vedclass · Answer

(D) The general term in the expansion of $(2+\sqrt{3})^8$ is given by $T_{r+1} = { }^8 C_r (2)^{8-r} (\sqrt{3})^r$. For the term to be rational,$r$ must be an even integer,i.e.,$r \in \{0, 2, 4, 6, 8\}$. The sum of rational terms is: $S = { }^8 C_0 (2)^8 + { }^8 C_2 (2)^6 (\sqrt{3})^2 + { }^8 C_4 (2)^4 (\sqrt{3})^4 + { }^8 C_6 (2)^2 (\sqrt{3})^6 + { }^8 C_8 (\sqrt{3})^8$ $S = 1 \cdot 256 + 28 \cdot 64 \cdot 3 + 70 \cdot 16 \cdot 9 + 28 \cdot 4 \cdot 27 + 1 \cdot 81$ $S = 256 + 5376 + 10080 + 3024 + 81$ $S = 18817$

The sum of all rational terms in the expansion of $(2+\sqrt{3})^8$ is

Similar Questions

If the coefficient of $x^{8}$ in $\left(a x^{2}+\frac{1}{b x}\right)^{13}$ is equal to the coefficient of $x^{-8}$ in $\left(a x-\frac{1}{b x^{2}}\right)^{13},$ then $a$ and $b$ will satisfy the relation

If the value of $C_{0}+2 \cdot C_{1}+3 \cdot C_{2}+\ldots+(n+1) \cdot C_{n}=576$,then $n$ is equal to

Let $n$ be a positive even integer. If the ratio of the largest coefficient and the $2^{nd}$ largest coefficient in the expansion of $(1+x)^{n}$ is $11:10$,then the number of terms in the expansion of $(1+x)^{n}$ is:

The number of integral terms in the expansion of $(7^{1/3} + 11^{1/9})^{6561}$ is:

Find $a$ if the coefficients of $x^{2}$ and $x^{3}$ in the expansion of $(3+ax)^{9}$ are equal.

Vedclass Test Series

Exam Paper Generator

Online Exam Module