Найти сумму n первых членов геометрической прогрессии, b1=-2 q=0.5 n=5 b1=-5 q=-2/3 n=5. Created by Temka15. algebra-ru

3 n=5...

Temka15 @Temka15

July 2022 1 10 Report

Найти сумму n первых членов геометрической прогрессии, b1=-2 q=0.5 n=5 b1=-5 q=-2/3 n=5

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dtnth

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$b_1=-2; q=0.5; n=5;\\ S_n=b_1*\frac{q^n-1}{q-1};\\ S_5=-2*\frac{0.5^5-1}{0.5-1}=-3.875$

$b_1=-5; q=-\frac{2}{3}; n=5;\\ S_n=b_1*\frac{1-q^n}{1-q};\\ S_5=-5*\frac{1-(-\frac{2}{3})^5}{1-(-\frac{2}){3}}=\\ -5*\frac{1+\frac{2^5}{3^5}}{1+\frac{2}{3}}=\\ -5*\frac{(3^5+2^5)*3}{3^5*(3+2)}=\\ -\frac{3^5+2^5}{3^4}=\\ -\frac{243+32}{81}=\\ -\frac{275}{81}$

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