What is \sum_{r=0}^{n}2^{r}C(n,r) equal to ?
- A. 2^{n}
- B. 3^{n} ✓
- C. 2^{2n}
- D. 3^{2n}
Correct Answer: B. 3^{n}
Explanation
According to the Binomial theorem, the expansion of (1+x)^n is \sum_{r=0}^{n} C(n,r) x^r. Substituting x=2 into this formula gives \sum_{r=0}^{n} C(n,r) 2^r = (1+2)^n = 3^n.
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