M Moistwh New member Joined Mar 16, 2019 Messages 10 May 14, 2019 #1 I need to find if the following series converges or diverges But I can't get rid of the constant 5 Help

I need to find if the following series converges or diverges But I can't get rid of the constant 5 Help

pka Elite Member Joined Jan 29, 2005 Messages 8,444 May 14, 2019 #2 Moistwh said: I need to find if the following series converges or diverges View attachment 12122 Click to expand... Use the ratio test. \(\displaystyle \sum\limits_{k = 0}^\infty {\frac{{{2^{k + 1}} - 5}}{{{3^k}}}} = 2\sum\limits_{k = 0}^\infty {\frac{{{2^k}}}{{{3^k}}} - 5} \sum\limits_{k = 0}^\infty {\frac{1}{{{3^k}}}} \)

Moistwh said: I need to find if the following series converges or diverges View attachment 12122 Click to expand... Use the ratio test. \(\displaystyle \sum\limits_{k = 0}^\infty {\frac{{{2^{k + 1}} - 5}}{{{3^k}}}} = 2\sum\limits_{k = 0}^\infty {\frac{{{2^k}}}{{{3^k}}} - 5} \sum\limits_{k = 0}^\infty {\frac{1}{{{3^k}}}} \)