Mathematics
aleciapusey
9

can anyone help??? Identify whether the series below is a convergent or divergent geometric series and find the sum, if possible.

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(1) Answers
nikolak

[latex]\sum\limits^{\infty}_{i = 1}{8(\frac{5}{6})^{i - 1}} = 8(\frac{5}{6})^{1 - 1} + 8(\frac{5}{6})^{2 - 1} + 8(\frac{5}{6})^{3 - 1} +...[/latex] [latex]\sum\limits^{\infty}_{i = 1}{8(\frac{5}{6})^{i - 1}} = 8(\frac{5}{6})^{0} + 8(\frac{5}{6})^{1} + 8\frac{5}{6})^{2} +...[/latex] [latex]\sum\limits^{\infty}_{i = 1} = 8(1) + 8(\frac{5}{6}) + 8(\frac{25}{36})+...[/latex] [latex]\sum\limits^{\infty}_{i = 1} = 8 + 6\frac{2}{3} + 5\frac{5}{9} +...[/latex] [latex]\sum\limits^{\infty}_{i = 1} = 20\frac{2}{9} +...[/latex] The series is a divergent geometric series.

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