\(P=4^{25}\cdot\left(\dfrac{1}{2}-\dfrac{1}{3}\right)\cdot\left(\dfrac{1}{2}-\dfrac{1}{5}\right)\cdot\left(\dfrac{1}{2}-\dfrac{1}{7}\right)\cdot...\cdot\left(\dfrac{1}{2}-\dfrac{1}{101}\right)\)
\(P=4^{25}\cdot\left(\dfrac{1}{2}\cdot\left(\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}-...+\dfrac{1}{101}\right)\right)\)
\(P=4^{25}\cdot\left(\dfrac{1}{2}\cdot\left(\dfrac{1}{101}-\dfrac{1}{3}\right)\div2+1\right)\)
\(P=4^{25}\cdot\left(\dfrac{1}{2}\cdot\dfrac{1}{50}\right)\)
\(P=4^{25}\cdot\dfrac{1}{100}\)
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