Question:medium

The constant term in the expansion of \( \left(1+\frac{1}{x}\right)^{20} \left(30x(1+x)^{29} + (1+x)^{30}\right) \) is

Show Hint

To find the coefficient of \( x^k \) in \( x^m (1+x)^n \), you simply need to find the coefficient of \( x^{k-m} \) in the binomial expansion of \( (1+x)^n \), which is \( {}^{n}C_{k-m} \). Be careful with negative powers.
Updated On: Mar 26, 2026
  • \( {}^{50}C_{20} + 30 \cdot {}^{50}C_{29} \)
  • \( {}^{50}C_{19} + 30 \cdot {}^{49}C_{19} \)
  • \( {}^{50}C_{20} + 30 \cdot {}^{49}C_{20} \)
  • \( {}^{50}C_{20} + 30 \cdot {}^{49}C_{19} \)
Show Solution

The Correct Option is D

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