The sum of all rational terms in the expansion of ( 12^5 + 15^3)^15 is equal to:

The sum of all rational terms in the expansion of ( 12^5 + 15^3)^… — Solution | JEE Mathematics

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The sum of all rational terms in the expansion of $\left(\frac{1}{2^5} + \frac{1}{5^3}\right)^{15}$ is equal to:

A
$3133$
B
$633$
C
$931$
D
$6131$

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: Find the sum of all rational terms in the expansion of $\left(\frac{1}{2^5} + \frac{1}{5^3}\right)^{15}$ .

Find: The numerical sum of all rational terms.

The solution is unrelated to the given question and discusses coefficients of powers of $x$ in another expansion. Hence, it cannot be used to derive the answer for this question.

Using the source answer key, the correct option is A, which corresponds to $3133$ .

Common mistakes

Treating every term in the binomial expansion as irrational. Here, one must check which powers produce rational values before summing them.
Confusing the exponents on $2$ and $5$ inside the terms. The expressions are $\frac{1}{2^5}$ and $\frac{1}{5^3}$ , so careless rewriting changes the expansion.
Adding coefficients instead of adding the actual rational terms. The question asks for the sum of rational terms, not the sum of binomial coefficients.

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Answer

Step-by-step solution

Common mistakes

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