\(A=\dfrac{16}{7\times9}+\dfrac{16}{9\times11}+...+\dfrac{16}{97\times99}\)
\(A=8\times\left(\dfrac{2}{7\times9}+\dfrac{2}{9\times11}+...+\dfrac{2}{97\times99}\right)\)
\(A=8\times\left(\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(A=8\times\left(\dfrac{1}{7}-\dfrac{1}{99}\right)\)
\(A=8\times\dfrac{92}{693}\)
\(A=\dfrac{736}{693}\)
\(A=\dfrac{16}{7x9}+\dfrac{16}{9x11}+\dfrac{16}{11x13}+...+\dfrac{16}{97x99}\\ A:8=\dfrac{2}{7x9}+\dfrac{2}{9x11}+\dfrac{2}{11x13}+...+\dfrac{2}{97x99}\\ A:8=\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}+...+\dfrac{1}{97}-\dfrac{1}{99}\\ A:8=\dfrac{1}{7}-\dfrac{1}{99}\\ A=\left(\dfrac{1}{7}-\dfrac{1}{99}\right)\times8=\dfrac{736}{693}\)
\(A=\dfrac{16}{7\times9}+\dfrac{16}{9\times11}+...+\dfrac{16}{97\times99}\\ A=8\times\left(\dfrac{1}{7}-\dfrac{1}{9}\right)+8\times\left(\dfrac{1}{9}-\dfrac{1}{11}\right)+...+8\times\left(\dfrac{1}{97}-\dfrac{1}{99}\right)\\ A=8\times\left(\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\\ A=8\times\left(\dfrac{1}{7}-\dfrac{1}{99}\right)\\ A=8\times\dfrac{92}{693}\\ A=\dfrac{736}{693}\)
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