Does the following infinite geometric series diverge or converge? 6 + 24 + 96 + 384 +...?
A(n) = (3/2) * 4^n ................. n S(n) = (3/2) ∑ 4^k = (3/2) (4/3) 4^(n-1) ................. k=1 Lim (1/2) * 4^(n) = ∞ n→∞ Ans: A
Does this infinite geometric series diverge or converge? Explain.?
If you factor out 1/5, you get (1/5)*(1 + 1/2 + 1/4 + 1/8 + ... ) So the nth term in the sum is (1/5)*(1/2)^n for n = 0,1,2,... Any geometric series with terms of the form a*x^n converges to a/(1-x) when |x| < 1. In this case, a = 1/5 and x = 1/2. Since |1/2| = 1/2 < 1, the series converges to the value (1/5)/(1-1/2) = 2/5 so the anwer is C.
Does the infinite geometric series converge or diverge?
D yes it converges and the sum will be 2/5
Where does the geometric series converge from n=1 to infinity?
⑴ Sum of GP to n terms=S(n)=[n=1 ,n=n]∑ar^(n-1) =a+ar+ar²+ar³+.....+ar^(n-1)= a(1-r^n)/(1-r)⑵ when |r|<1 , n→∞,r^n→0,S(n)→S(∞)=a(1–0)/(1-r)=a/(1-r)
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.?
Convergent geometric series. Ratio = 0.4 Sum = 1/(1-0.4) = 5/3 = 1.6666...
Algebra 2 Geometric Series Converge and Diverge question! Help me Understand.?
Does the following infinite series diverge or converge? 1/3-2/9+4/27-8/81+... A. It diverges, it has a sum. B. It converges, it has a sum C. It diverges, it does not have a sum D. It converges, it does not have a sum I have trouble understanding this question. I dont even understand what i dont understand. I'm not sure what the question means if it has a sum or doesn't, wont it always have a sum? And when I evaluate the series it gives me a fraction. Does a fraction converge?
Does [math]\displaystyle \sum^{\infty}_{n=1} \frac{9^n}{3+10^n}[/math] converge or diverge?
You can’t split a fraction like that. [math]\frac{a}{b+c} \neq \frac{a}{b} + \frac{a}{c}[/math]. Simple as that.
What is the differences between converges and diverges?
A series is a limit of partial sums.[math]\sum_{n=0}^\infty a_n = \lim_{N\to\infty} \sum_{n=0}^N a_n [/math]The series converges when the limit exists and is finite. Otherwise, we say the series diverges. There are two things to look for when wondering if the series diverges. First, the sum could go to infinity such as [math]\sum_{n=0}^\infty 1[/math] or [math]\sum_{n=1}^\infty \frac{1}{n}[/math] both diverge[math].[/math] Second, the limit could fail to exist because the sum bounces around. For example, [math]\sum_{n=0}^\infty (-1)^{n}[/math] diverges.