Bn-геометрическая прогрессия. B4=1_25; В5=1_125. Найдите S5.

[latex]b_4=\frac{1}{25}\\ b_5=\frac{1}{125}\\ b_5=qb_4=\ \textgreater \ q=\frac{b_5}{b_4}=\frac{\frac{1}{125}}{\frac{1}{25}}=\frac{25}{125}=\frac{1}{5}\\ b_4=b_1q^3=\ \textgreater \ b_1=\frac{b_4}{q^3}=\frac{\frac{1}{25}}{\frac{1}{125}}=\frac{125}{25}=5\\ S_5=\frac{b_1(1-q^5)}{1-q}=\frac{5(1-\frac{1}{3125})}{1-\frac{1}{5}}=\frac{5*\frac{3124}{3125}}{\frac{4}{5}}=\frac{25*3124}{4*3125}=\frac{781}{125}[/latex]