BẠN ƠI BẠN CHỈ CẦN TÁCH RIÊNG THÀNH 2 VỀ RỒI GIẢI NHÉ
Đặt \(A=\left(\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...+\frac{1}{44.49}\right).\frac{1-3-5-7-...-49}{89}\)
\(\Rightarrow A=\frac{1}{5}.\left(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{44.49}\right).\frac{1-\left(3+5+7+...+49\right)}{89}\)
\(\Rightarrow A=\frac{1}{5}.\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{44}-\frac{1}{49}\right).\frac{1-\frac{\left(49+3\right).24}{2}}{89}\)
\(\Rightarrow A=\frac{1}{5}.\left(\frac{1}{4}-\frac{1}{49}\right).\frac{1-\frac{1248}{2}}{89}\)
\(\Rightarrow A=\frac{1}{5}.\frac{45}{196}.\frac{1-624}{89}\)
\(\Rightarrow A=\frac{1}{5}.\frac{45}{196}.\left(-\frac{623}{89}\right)\)
\(\Rightarrow A=\frac{1}{5}.\frac{45}{196}.\left(-7\right)\)
\(\Rightarrow A=\frac{9}{196}.\left(-7\right)\)
\(\Rightarrow A=-\frac{9}{28}.\)
Vậy \(A=-\frac{9}{28}.\)
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