Question

5.Efectuează calculele și scrie rezultatul sub forma de fractie ireductibila:​

Answer 1

Sper că te-am ajutat!!!

Answer 2

Răspuns:

Explicație pas cu pas:

$\dfrac{1}{27} + \dfrac{2}{27} + \dfrac{3}{27} + ... + \dfrac{26}{27} = \dfrac{1+2+3+...+26}{27} = \dfrac{\dfrac{26 \cdot 27}{2} }{27} = \dfrac{26 \cdot 27}{2 \cdot 27} =\bf 13$

$\dfrac{1}{103} + \dfrac{2}{103} + \dfrac{3}{103} + ... + \dfrac{103}{103} = \dfrac{1+2+3+...+103}{103} = \dfrac{\dfrac{103 \cdot 104}{2} }{103} = \dfrac{103 \cdot 104}{2 \cdot 103} =\bf 52$

$100 + \dfrac{1}{100} + \dfrac{2}{100} + \dfrac{3}{100} + ... + \dfrac{99}{100} = 100 + \dfrac{1+2+3+...+99}{100} = 100 + \dfrac{\dfrac{99 \cdot 100}{2} }{100} = 100 + \dfrac{99 \cdot 100}{2 \cdot 100} = 100 + \dfrac{99}{2} = \dfrac{200 + 99}{2} = \bf \dfrac{299}{2}$

$\dfrac{1}{2} + \dfrac{1}{2^{2}} + \dfrac{1}{2^{3}} + \dfrac{1}{2^{4}} + \dfrac{1}{2^{5}} + \dfrac{1}{2^{6}} = \dfrac{2^{5}}{2^{6}} + \dfrac{2^{4}}{2^{6}} + \dfrac{2^{3}}{2^{6}} + \dfrac{2^{2}}{2^{6}} + \dfrac{2}{2^{6}} + \dfrac{1}{2^{6}} = \dfrac{32+16+8+4+2+1}{2^{6}} = \bf \dfrac{63}{64}$

$\dfrac{1}{5} + \dfrac{11}{55} + \dfrac{111}{555} + ... + \dfrac{1111111}{5555555} = \dfrac{1}{5} + \dfrac{11}{5 \cdot 11} + \dfrac{111}{5 \cdot 111} + ... + \dfrac{1111111}{5 \cdot 1111111} = \underbrace{\dfrac{1}{5} + \dfrac{1}{5}+ \dfrac{1}{5} + ... + \dfrac{1}{5}}_{7} = 7 \cdot \dfrac{1}{5} = \bf \dfrac{7}{5}$

$\dfrac{1}{2022} + \dfrac{2}{2022} + \dfrac{3}{2022} + ... + \dfrac{2021}{2022} = \dfrac{1+2+3+...+2021}{2022} = \dfrac{\dfrac{2021 \cdot 2022}{2} }{2022} = \dfrac{2021 \cdot 2022}{2 \cdot 2022} =\bf \dfrac{2021}{2}$