COMEDK · Maths · 7. Binomial Theorem
The coefficient of \(x^{10}\) in the expansion of \(1+(1+x)+\ldots+(1+x)^{20}\) is
- A \({ }^{19} C_{9}\)
- B \({ }^{20} C_{10}\)
- C \({ }^{21} C_{11}\)
- D \({ }^{22} C_{12}\)
Answer & Solution
Correct Answer
(C) \({ }^{21} C_{11}\)
Step-by-step Solution
Detailed explanation
The given expression is a geometric series with first term \(a = 1\), common ratio \(r = (1+x)\), and number of terms \(n = 21\). The sum of the series is \(S = a \dfrac{r^n - 1}{r - 1} = 1 \times \dfrac{(1+x)^{21} - 1}{(1+x) - 1} = \dfrac{(1+x)^{21} - 1}{x}\). We need the…
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