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\(=\)\(\left(\frac{1}{125}-\frac{1}{1^3}\right)\) \(.\) \(\left(\frac{1}{125}-\frac{1}{2^3}\right)\) \(.\) \(\left(\frac{1}{125}-\frac{1}{3^3}\right)\) \(.\) \(\left(\frac{1}{125}-\frac{1}{5^3}\right)\)\(...\) \(\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\) \(\left(\frac{1}{125}-\frac{1}{1^3}\right)\) \(.\) \(\left(\frac{1}{125}-\frac{1}{2^3}\right)\) \(.\) \(\left(\frac{1}{125}-\frac{1}{3^3}\right)\) \(.\) \(0\) \(....\) \(\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\) \(0\)
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\(\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)...\left(\frac{1}{125}-\frac{1}{5^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)...0...\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=0\)
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\(A=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)\left(\frac{1}{125}-\frac{1}{3^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)\\ A=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)\left(\frac{1}{125}-\frac{1}{3^3}\right)\left(\frac{1}{125}-\frac{1}{4^3}\right)\left(\frac{1}{125}-\frac{1}{5^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)\\ A=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)\left(\frac{1}{125}-\frac{1}{3^3}\right)\left(\frac{1}{125}-\frac{1}{4^3}\right)\left(\frac{1}{125}-\frac{1}{125}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)\\ A=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)\left(\frac{1}{125}-\frac{1}{3^3}\right)\left(\frac{1}{125}-\frac{1}{4^3}\right)\cdot0\cdot...\left(\frac{1}{125}-\frac{1}{25^3}\right)\\ A=0\)
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\(B=\left(\dfrac{1}{125}-\dfrac{1}{1^3}\right).\left(\dfrac{1}{125}-\dfrac{1}{2^3}\right)....\left(\dfrac{1}{125}-\dfrac{1}{5^3}\right).....\left(\dfrac{1}{125}-\dfrac{1}{25^3}\right)\\ =\left(\dfrac{1}{125}-\dfrac{1}{1^3}\right).\left(\dfrac{1}{125}-\dfrac{1}{2^3}\right)....0.....\left(\dfrac{1}{125}-\dfrac{1}{25^3}\right)\\ =0\)
\(B=\left(\dfrac{1}{125}-\dfrac{1}{1^3}\right).\left(\dfrac{1}{125}-\dfrac{1}{2^3}\right).\left(\dfrac{1}{125}-\dfrac{1}{3^3}\right).....\left(\dfrac{1}{125}-\dfrac{1}{25^3}\right)\\ =\left(\dfrac{1}{125}-\dfrac{1}{1^3}\right).\left(\dfrac{1}{125}-\dfrac{1}{2^3}\right).\left(\dfrac{1}{125}-\dfrac{1}{3^3}\right)....\left(\dfrac{1}{125}-\dfrac{1}{5^3}\right).....\left(\dfrac{1}{125}-\dfrac{1}{25^3}\right)\\ =\left(\dfrac{1}{125}-\dfrac{1}{1^3}\right).\left(\dfrac{1}{125}-\dfrac{1}{2^3}\right).\left(\dfrac{1}{125}-\dfrac{1}{3^3}\right)....\left(\dfrac{1}{125}-\dfrac{1}{125}\right).....\left(\dfrac{1}{125}-\dfrac{1}{25^3}\right)\\ =\left(\dfrac{1}{125}-\dfrac{1}{1^3}\right).\left(\dfrac{1}{125}-\dfrac{1}{2^3}\right).\left(\dfrac{1}{125}-\dfrac{1}{3^3}\right)....0.....\left(\dfrac{1}{125}-\dfrac{1}{25^3}\right)=0\)