Tính tổng S = \(2015+\frac{2015}{1+2}+\frac{2015}{1+2+3}+...+\frac{2015}{1+2+3+...+2016}\)
Những câu hỏi liên quan
Tính tổng S = \(2015+\frac{2015}{1+2}+\frac{2015}{1+2+3}+...+\frac{2015}{1+2+3+...+2016}\)
Tính tổng:
\(S=2015+\frac{2015}{1+2}+\frac{2015}{1+2+3}+....+\frac{2015}{1+2+3+...+2016}\)
Tính nhanh : \(\frac{2017+\frac{1}{2016}+\frac{2}{2015}+\frac{3}{2014}+...+\frac{2015}{2}+\frac{2016}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2015}+\frac{1}{2016}}\)
RGBT:
E=\(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{2015\sqrt{2014}+2014\sqrt{2015}}+\frac{1}{2016\sqrt{2015}+2015\sqrt{2016}}\)
Ta có:
\(\frac{1}{\left(n+1\right)\sqrt{n}+n\sqrt{n+1}}=\frac{1}{\sqrt{n\left(n+1\right)}\left(\sqrt{n+1}+\sqrt{n}\right)}\)
\(=\frac{\left(\sqrt{n+1}-\sqrt{n}\right)}{\sqrt{n\left(n+1\right)}}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}\)
Thế vô bài toán được
\(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{2016\sqrt{2015}+2015\sqrt{2016}}\)
\(=\frac{1}{\sqrt{1}}-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{2015}}-\frac{1}{\sqrt{2016}}\)
\(=1-\frac{1}{\sqrt{2016}}\)
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Tính tổng: S= 2016+\(\frac{2016}{1+2}+\frac{2016}{1+2+3}+...+\frac{2016}{1+2+3+...+2015}\)
giúp mình nha
\(\frac{2.1+1}{\left(1+1\right)^2}+\frac{2.2+1}{\left(2^2+2\right)^2}+\frac{2.3+1}{\left(3^3+3\right)^2}+....+\frac{2.2015+1}{\left(2015^2+2015\right)^2}+\frac{2.1016+1}{\left(2016^2+2016\right)^2}\)
tính tổng . ai giúp vs
Tinh:
S=2015+\(\frac{2015}{1+2}\)+\(\frac{2015}{1+2+3}\)+\(\frac{2015}{1+2+3+4}\)+...+\(\frac{2015}{1+2+3+...+2016}\)
Tinh:
S=2015+\(\frac{2015}{1+2}\)+\(\frac{2015}{1+2+3}\)+...+\(\frac{2015}{1+2+3+...+2016}\)
TÍNH TỔNG S:\(1-\frac{1}{3}+\frac{1}{^{3^2}}-\frac{1}{3^3}+.......-\frac{1}{3^{2015}}+\frac{1}{3^{2016}}\)
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