The following series are geometric series.
Determine whether each series converges or not.
For the series which converge, enter the sum of the series.
For the series which diverges enter "DNE" (without quotes).
(a)
∑ n = 1 ∞ 9 n 8 n = \displaystyle {\sum_{{{n}={1}}}^{{\infty}}}{\frac{{{9}^{{n}}}}{{{8}^{{n}}}}}= n = 1 ∑ ∞ 8 n 9 n = Preview Question 6 Part 1 of 6 ,
(b)
∑ n = 2 ∞ 1 3 n = \displaystyle {\sum_{{{n}={2}}}^{{\infty}}}{\frac{{{1}}}{{{3}^{{n}}}}}= n = 2 ∑ ∞ 3 n 1 = Preview Question 6 Part 2 of 6 ,
(c)
∑ n = 0 ∞ 3 n 8 2 n + 1 = \displaystyle {\sum_{{{n}={0}}}^{{\infty}}}{\frac{{{3}^{{n}}}}{{{8}^{{{2}{n}+{1}}}}}}= n = 0 ∑ ∞ 8 2 n + 1 3 n = Preview Question 6 Part 3 of 6 ,
(d)
∑ n = 5 ∞ 8 n 9 n = \displaystyle {\sum_{{{n}={5}}}^{{\infty}}}{\frac{{{8}^{{n}}}}{{{9}^{{n}}}}}= n = 5 ∑ ∞ 9 n 8 n = Preview Question 6 Part 4 of 6 ,
(e)
∑ n = 1 ∞ 8 n 8 n + 4 = \displaystyle {\sum_{{{n}={1}}}^{{\infty}}}{\frac{{{8}^{{n}}}}{{{8}^{{{n}+{4}}}}}}= n = 1 ∑ ∞ 8 n + 4 8 n = Preview Question 6 Part 5 of 6 ,
(f)
∑ n = 1 ∞ 8 n + 3 n 9 n = \displaystyle {\sum_{{{n}={1}}}^{{\infty}}}{\frac{{{8}^{{n}}+{3}^{{n}}}}{{{9}^{{n}}}}}= n = 1 ∑ ∞ 9 n 8 n + 3 n = Preview Question 6 Part 6 of 6 .
Submit Try a similar question
[more..]
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)