# geometric

1. ### Geometric Series - Converge or Diverge - # 11

Converge or diverge? \displaystyle\sum_{n=0}^{\infty} (-1)^{n}\dfrac{5}{4^{n}} What would be the strategy in finding r?
2. ### Geometric Series - Converge or Diverge - # 10

Converge or diverge? \displaystyle\sum_{n=0}^{\infty} \cos n\pi What would be the strategy in finding r?
3. ### Geometric Series - Converge or Diverge - # 9

Converge or diverge? \displaystyle\sum_{n=0}^{\infty} \dfrac{\cos n\pi}{5^{n}} What would be the strategy in finding r?
4. ### Geometric Series - Converge or Diverge - # 8

Converge or diverge? \displaystyle\sum_{n=1}^{\infty} (-1)^{n+1} \dfrac{3}{2^{n}} What would be r?
5. ### Geometric Series - Converge or Diverge - # 7

Converge or diverge? \displaystyle\sum_{n=1}^{\infty} \dfrac{n!}{1000^{n}} What is r, in this factorial situation?
6. ### Geometric Series - Converge or Diverge - # 6

Converge or diverge? \displaystyle\sum_{n=1}^{\infty} (1 - \dfrac{1}{n})^{n} How should this be read? What would be r?
7. ### Geometric Series - Converge or Diverge - # 5

Converge or diverge? \displaystyle\sum_{n=1}^{\infty} \ln(\dfrac{n}{n+1}) What would be r?
8. ### Geometric Series - Converge or Diverge - # 4

Converge or Diverge? \displaystyle\sum_{n=0}^{\infty} e^{-2n} Would r = 1, and a = 1? What if it was \displaystyle\sum_{n=1}^{\infty} e^{-2n} ??
9. ### Geometric Series - Converge or Diverge - # 3

Converge or diverge? \displaystyle\sum_{n=1}^{\infty} \dfrac{2}{10^{n}} What is r? It's confusing because n is in the denominator only. I'm thinking a might be \dfrac{1}{10}
10. ### Geometric Series - Converge or Diverge - # 2

Does this series converge or diverge? (Post edited) \displaystyle\sum_{n=0}^{\infty} (\dfrac{1}{\sqrt{2}})^{n} r = \dfrac{1}{\sqrt{2}}, but what is a? I'm thinking a = 1
11. ### Geometric Series - nth Partial Sum

Find a formula for the nth partial sum of the series. If it converges find the sum. 1 - \dfrac{1}{2} + \dfrac{1}{4} - \dfrac{1}{8} +....+(-1)^{n-1}\dfrac{1}{2^{n-1}} + ... The answer is s_{n} = \dfrac{1 - (-1/2)^{n} }{1-(-1/2) } and it converges to \dfrac{2}{3} We can tell from looking...
12. ### Geometric Series Problem - Repeating Decimals

Show as a ratio of two integers. 0.23 with a bar (not written) on top of the 2 and 3. The answer in the book is \dfrac{23}{99} What is the procedure to get this?
13. ### Geometric sum

Hello, I am not really sure what to do with this.
14. ### Geometric Series - # 2

How would you calculate the next terms in the series?
15. ### Geometric Series

What is the math reasoning behind making a = \dfrac{1}{4} ? For instance, how does the power of n stuff work?
16. ### Sum of Infinite Geometric Series Help?

I was given this equation Sum=2+4+8+...2^n+2^n+1+... and the sum of this infinite geometric series is -2 Can someone please help explain why?
17. ### Geometric Proofs

What is the best way to learn direct and indirect geometric proofs using the statements versus reasons chart through self-study?
18. ### Geometric distributions

Howdy :) I am trying to solve but unsure of what I should be doing for part (ii). I have worked out p and the probability generating function of X for part (i). Is this information meant to help me for part (ii)? As I am unsure how I get to the point of deciding what the probability...
19. ### Testing whether or not a series is geometric

Above is the question as to whether or not E^infinity n=2 2^n/5^2n is geometric or not. I used the an+1/an formula to check and found out that it was indeed geometric, however my answer came out to 1/5 and not 2/25 as in the example. Where did the example even get the additional +2 on the...
20. ### Euclidean Geometric Proof regarding Triangles

Hello, This is related to altitudes, medians and bisectors in a triangle: I'm struggling to solve this proof - In triangle ABC where AB is not equal to AC, and AH, AD, AM are the altitude, bisector, and median, respectively, prove that point D will always fall between H and M. I've set...