Question

calcule a soma dos infinitos termos de cada pg

a) (15,10,20/3,...)

b) ( -π,- π/2,- π/4,...)


PFV É PRA AMANHA

Answer 1

Resposta:

Soma da P.G infinita quando temos a₁ e q

$S_n={a_1\over1-q}\\ \\ a)\\ \\ a_1=15\\ q=a_2\div a_1\\ q=10\div15\\ \\ q={10\over15}={2\over3}\\ \\ logo\\ \\ S_n={15\over1-{2\over3}}\\ \\ S_n=15\div({3-2\over3})\\ \\ S_n=15\div({1\over3})\\ \\ S_n=15\times3\\ \\ S_n=45$

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$b)\\ a_1=-\pi \\ \\ q=-{\pi \over2}\div(-\pi) \\ \\ q=(-{\pi \over2})\times(-{1\over\pi })\\ \\ q={1\over2}\\ \\ S_n={-\pi \over1-{1\over2}}\\ \\ S_n=-\pi \div({2-1\over2})\\ \\ S_n=-\pi \div{1\over2}\\ \\ S_n=-\pi \times2\\ \\ S_n=-2\pi$