tính nhanh.
1/3+1/6+1/10 +1/15+...+1/55
e cảm ơn ạ !
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Đặt \(A=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+....+\dfrac{1}{78}\)
⇒\(\dfrac{1}{2}A=\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{156}\)
⇒\(\dfrac{1}{2}A=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{12.13}\)
⇒\(\dfrac{1}{2}A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}+...+\dfrac{1}{12}-\dfrac{1}{13}\)
⇒\(\dfrac{1}{2}A=\dfrac{1}{2}-\dfrac{1}{13}\)\(=\dfrac{11}{26}\)
⇒\(A=\dfrac{11}{26}:\dfrac{1}{2}\)
⇒\(A=\dfrac{11}{13}\)
(7/111 - 4/33 + 9/37).(1/2 - 1/3 -1/6)
= (7/111 - 4/33 + 9/37).0
= 0
(7/111 - 4/33 + 9/37).(1/2 - 1/3 - 1/6)
= (7/111 - 4/33 + 9/37).0
= 0
=2*(1/6+1/12+1/20+...+1/380)
=2*(1/2*3+1/3*4+1/4*5+...+1/19*20)
=2*(1/2-1/3+1/3-1/4+1/4-1/5+...+1/19-1/20)
=2*(1/2-1/20)
=2*(10/20-1/20)
=2*9/20
=18/20
=9/10
Sửa đề:
B = 1 - 3 - 5 + 7 + 9 - 11 - 13 + 15 + ... + 2019 - 2021 - 2023 + 2025 + 2027
= (1 - 3 - 5 + 7) + (9 - 11 - 13 + 15) + ... + (2019 - 2021 - 2023 + 2025) + 2027
= 0 + 0 + ... + 0 + 2027
= 2027
Nhầm xíu :>>
Đặt \(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{55}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{10\times11}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{2}-\frac{1}{11}\Rightarrow\frac{1}{2}A=\frac{9}{22}\Rightarrow A=\frac{9}{11}\)
Đặt \(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{55}\)
\(\Rightarrow2A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}\)
\(\Rightarrow2A=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{10\times11}\)
\(\Rightarrow2A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)
\(\Rightarrow2A=\frac{1}{2}-\frac{1}{11}\Rightarrow2A=\frac{9}{22}\Rightarrow A=\frac{9}{44}\)