Question

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 9 - 11 + frac{121}{9} - frac{1331}{81} + ... Step 1 To see $9 - 11 + frac{121}{9} - frac{1331}{81} + ...$ as a geometric series, we must express it as $sum_{n=1}^{infty} ar^{n-1}$. For any two successive terms in the geometric series $sum_{n=1}^{infty} ar^{n-1}$, the ratio of the two terms, $frac{ar^n}{ar^{n-1}}$, simplifies into an algebraic expression given by $r$. Step 2 In our series $9 - 11 + frac{121}{9} - frac{1331}{81} + ...$, the ratio $frac{-frac{1331}{81}}{frac{121}{9}}$ is $r = -frac{11}{9}$. Step 3 In the series $9 - 11 + frac{121}{9} - frac{1331}{81} + ...$, the $n = 3$ term is $frac{121}{9}$. If this is to equal $ar^2 = a(-frac{11}{9})^2$, then $a = 9$. Step 4 Similarly, $-frac{1331}{81} = ext{________}(-frac{11}{9})^3$. Submit Skip (you cannot come back)

          Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
9 - 11 + frac{121}{9} - frac{1331}{81} + ...
Step 1
To see $9 - 11 + frac{121}{9} - frac{1331}{81} + ...$ as a geometric series, we must express it as $sum_{n=1}^{infty} ar^{n-1}$.
For any two successive terms in the geometric series $sum_{n=1}^{infty} ar^{n-1}$, the ratio of the two terms, $frac{ar^n}{ar^{n-1}}$, simplifies into an algebraic expression given by $r$.
Step 2
In our series $9 - 11 + frac{121}{9} - frac{1331}{81} + ...$, the ratio $frac{-frac{1331}{81}}{frac{121}{9}}$ is $r = -frac{11}{9}$.
Step 3
In the series $9 - 11 + frac{121}{9} - frac{1331}{81} + ...$, the $n = 3$ term is $frac{121}{9}$.
If this is to equal $ar^2 = a(-frac{11}{9})^2$, then $a = 9$.
Step 4
Similarly, $-frac{1331}{81} = 	ext{________}(-frac{11}{9})^3$.
Submit Skip (you cannot come back)

$Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 9 - 11 + frac1219 - frac133181 + ... Step 1 To see 9 - 11 + frac1219 - frac133181 + ... as a geometric series, we must express it as sumn=1^infty ar^n-1. For any two successive terms in the geometric series sumn=1^infty ar^n-1, the ratio of the two terms, fracar^nar^n-1, simplifies into an algebraic expression given by r. Step 2 In our series 9 - 11 + frac1219 - frac133181 + ..., the ratio frac-frac133181frac1219 is r = -frac119. Step 3 In the series 9 - 11 + frac1219 - frac133181 + ..., the n = 3 term is frac1219. If this is to equal ar^2 = a(-frac119)^2, then a = 9. Step 4 Similarly, -frac133181 = ext(-frac119)^3. Submit Skip (you cannot come back)$

Added by Phillip F.

Question

Please give Ace some feedback