Question

b4=2/5, q=2/3. Знайти S5.​

Answer 1

Ответ: S₅=3³¹/₆₀.

Объяснение:

$b_4=\frac{2}{5} ;q=\frac{2}{3};S_5=?\\ b_4=b_1q^{3} =\frac{2}{5} \\ b_1=\frac{b_4}{q^3} =\frac{\frac{2}{5} }{(\frac{2}{3})^{3} } =\frac{\frac{2}{5} }{\frac{8}{27} }=\frac{2*27}{5*8}=\frac{27}{20}.\\S_5=\frac{27}{20} *\frac{1-(\frac{2}{3})^{5} }{1-\frac{2}{3} } =\frac{27}{20} *\frac{1-\frac{32}{243} }{\frac{1}{3} } =\frac{27}{20}*\frac{\frac{211}{243} }{\frac{1}{3} }=\frac{27}{20}*\frac{211}{81} =\frac{211}{60}=3\frac{31}{60} .$