Tính tổng sau:
$S_{n}=C_{n}^{0}+\frac{1}{2}C_{n}^{1}+\frac{1}{3}C_{n}^{2}+...+\frac{1}{1+n}C_{n}^{n}$
Tính tổng sau: $S_{n}=C_{n}^{0}+\frac{1}{2}C_{n}^{1}+\frac{1}{3}C_{n}^{2}+...+\frac{1}{1+n}C_
Started By Phuong Thu Quoc, 15-04-2014 - 21:38
#1
Posted 15-04-2014 - 21:38
Phuong Thu Quoc
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Trung úy
#2
Posted 15-07-2018 - 17:06
Hr MiSu
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Ta có: $(1+x)^{n}=\sum_{i=1}^{n}\binom{n}{i}x^{i} \Rightarrow \int_{0}^{1}(1+x)^{n}=\int_{0}^{1}\sum_{i=1}^{n}\binom{n}{i}x^{i} \Rightarrow \sum_{i=1}^{n} \frac{1}{i+1}.\binom{n}{i}=\frac{2^{n+1}}{n+1}-\frac{1}{n+1}$
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