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= 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 +...+ 1/14 - 1/15 + 1/15 - 1/16
= 1/4 - 1/16
= 3/16
Công thức : 1/ a x (a+1) = 1/a - 1/ a+1
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\(\frac{1}{1}=1\)
Viết lại: 1+2+1+2+3+...+1+2+...+10
=2+6+...+55
=163
Hội con 🐄 chúc bạn học tốt!!!
\(D=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+10}\)
\(D=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{\frac{\left[1+10\right]\cdot10}{2}}\)
\(D=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{55}\)
\(D=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{110}\)
\(\frac{D}{2}=2\left[\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}\right]\)
\(D=2\left[\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{10\cdot11}\right]\)
\(D=2\left[\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right]\)
\(D=2\left[\frac{1}{2}-\frac{1}{11}\right]\)
\(D=\frac{9}{11}\)
Vậy D = 9/11
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