Question

The constant term in the expansion of $(1+x)ᵐ(1+\frac1x)ⁿ$ is ________.

• A. ${}^{m+n}C_{m-1}$
• B. ${}^{m+n}C_{n}$
• C. ${}^{m+n}C_{m-n}$
• D. None of these

Hint:

The constant term in the expansion of $(1+x)$ is ____.

Answer 1

The Correct Option is B

Step 1: Simplify Expression
$(1+x)^m (1 + 1/x)^n = (1+x)^m (\frac{x+1}{x})^n = \frac{(1+x)^{m+n}}{x^n}$.
Step 2: Evaluation
Constant term in $\frac{(1+x)^{m+n}}{x^n}$ is the term independent of $x$.
Step 3: Finding the Term
This is equivalent to finding the coefficient of $x^n$ in $(1+x)^{m+n}$.
Step 4: Conclusion
Coefficient $= {}^{m+n}C_{n}$.
Hence, the Answer is: (B)