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[latex]1)\;\;\frac1{\not2}\cdot\frac{\not2}{\not3}\cdot\frac{\not3}{\not4}\cdot\frac{\not4}5=\frac15\\2)\;\;\frac6{\not7}\cdot\frac{\not7}{\not8}\cdot\frac{\not8}{\not9}\cdot\frac{\not9}{\not{10}}\cdot\frac{\not{10}}{11}=\frac6{11}\\3)\;\;\frac12\cdot\frac23\cdot\ldots\cdot\frac{23}{24}\cdot\frac{24}{25}=\frac1{25}[/latex] [latex]4)\;\;1\frac12\cdot1\frac13\cdot1\frac14\cdot1\frac15=\frac{\not3}2\cdot\frac{\not4}{\not3}\cdot\frac{\not5}{\not4}\cdot\frac6{\not5}=\frac62=3\\5)\;\;\left(1+\frac14\right)\cdot\left(1+\frac15\right)\cdot\left(1+\frac16\right)\cdot\left(1+\frac17\right)\cdot\left(1+\frac18\right)=\\=\frac{\not5}{4}\cdot\frac{\not6}{\not5}\cdot\frac{\not7}{\not6}\cdot\frac{\not8}{\not7}\cdot\frac{9}{\not8}=\frac94=2\frac14[/latex] [latex]6)\;\;\left(1-\frac12\right)\cdot\left(1-\frac13\right)\cdot\left(1-\frac14\right)\cdot\ldots\cdot\left(1-\frac1{99}\right)\cdot\left(1-\frac1{100}\right)=\\=\frac12\cdot\frac23\cdot\frac34\cdot\ldots\cdot\frac{98}{99}\cdot\frac{99}{100}=\frac1{100}=0,01[/latex]