$(1+x{)}^p(1+\frac{1}{x}{)}^q$ (p,q ধনাত্মক পূর্ণসংখ্যা) বিস্তৃতিতে x বর্জিত পদ নিচের কোনটি?

The question pertains to a mathematical expression involving two positive integers, p and q, and is asking which option represents the omitted term when expanding the given expression in terms of x.

The provided answer, which is:

is correct because:

    
• Summation Rules: In expressions involving powers of x in polynomial expansions, the coefficients of the terms can often be expressed in combinatorial form, specifically as C(n, k), representing combinations.
    
• Role of p and q: The term C(q) indicates that this expansion considers selections in terms of q elements paired with the sum of p and q.
    
• Omitted Terms: The selection C(q) suggests that the specific term being omitted correlates directly with how many times we select or arrange elements from the set defined by p and q.

Thus, the answer effectively captures the essential omitted term from the expansion concerning the influence of the integer values of p and q.

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