Lê Quốc Trần Anh Coordinator
03/08/2017 at 09:12-
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Denote B = 1.2 + 2.3 + 3.4 + ... + 97.98 + 98.99
\(\Rightarrow\) 3B = 1.2.3 + 2.3.3 + 3.4.3 + ... + 97.98.3 + 98.99.3
= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 97.98.(99 - 96) + 98.99.(100 - 97)
= (1.2.3 + 2.3.4 + 3.4.5 + ... + 97.98.99 + 98.99.100) - (1.2.3 + 2.3.4 + 96.97.98 + 97.98.99)
= 98.99.100
\(\Rightarrow B=\dfrac{98.99.100}{3}\)
\(\Rightarrow A=\dfrac{98.99.100}{3}-\dfrac{98.99}{2}=98.99.\left(\dfrac{100}{3}-\dfrac{1}{2}\right)\)
\(=98.99.\dfrac{197}{6}=318549\)
Lê Quốc Trần Anh selected this answer. -
یևσϞջ♱ɮևσϞ➪ȿ₂ 03/08/2017 at 10:00Let \(A=1^2+2^2+3^2+...+98^2\)
\(A=1\cdot1+2\cdot2+3\cdot3+...+98\cdot98\)
\(A=1\cdot\left(2-1\right)+2\cdot\left(3-1\right)+...+98\cdot\left(99-1\right)\)
\(A=\left(1\cdot2+2\cdot3+...+98\cdot99\right)-\left(1+2+...+98\right)\)
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