\(B\text{=}\dfrac{3}{1\times3}+\dfrac{3}{3\times5}+\dfrac{3}{5\times7}+...+\dfrac{3}{99\times101}\)
\(B\text{=}3\times\left(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+...+\dfrac{1}{99\times101}\right)\)
\(B\text{=}\dfrac{3}{2}\times\left(\dfrac{3-1}{1\times3}+\dfrac{5-3}{3\times5}+...+\dfrac{101-99}{99\times101}\right)\)
\(B\text{=}\dfrac{3}{2}\times\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)
\(B\text{=}\dfrac{3}{2}\times\left(1-\dfrac{1}{101}\right)\)
\(B\text{=}\dfrac{300}{202}\)
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