Question

Calculati :
(1/1•2+1/2•3+. . . +1/99•100):[(3/5)la puterea a 4•(3/5)la puterea a 3-a :(3/5)la puterea a 5-a

Answer 1

$\it ( \frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + ... + \frac{1}{99 \cdot 100} ):[( \frac{3}{5} )^{4} \cdot ( \frac{3}{5} )^{3} :( \frac{3}{5} )^{5} ] = ( \frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + ... + \frac{1}{99} - \frac{1}{100} ): \\ \\ :( \frac{3}{5} ) ^{4+ 3 - 5} = ( \: ^{100)} \frac{1}{1} - \frac{1}{100} ):( \frac{3}{5} )^{2} = ( \frac{100}{100} - \frac{1}{100} ):( \frac{3}{5} )^{2} = \frac{99}{100} : \frac{9}{25} = \frac{99}{100} \cdot \frac{25}{9} = \\ \\ = \frac{11}{4}$