For Which Positive Integers K Is the Following Series Convergent

Therefore the series converges when. And one could use Lopezs house rule here to see that this living goes toe one over fourth which is less than one.

Solved For Which Positive Integers K Is The Following Series Chegg Com

Sum _n1infty fracleftnright6leftknright I tried using RootRatio tests but that didnt work out.

. First we need a n 0. What is an integer. Approximate the sum of the series correct to four decimal places.

Infinite n 1 n2kn. 100 9 ratings for this solution. K 2 k2 k 2.

N2 n 1 kn. If K is bigger than two then the denominator has degree k which is also larger than to because youLL be multiplying K terms here. The positive integer that illustrates that theres convergence is k 2n.

N 1 k. Kn k kn k - 1 kn k - 2. And now I simplify.

It should be noted that an integer simply means a whole number that can be positive negative or zero. For series to be convergent the next inequality should be true by the Ratio Test. Not sure what to do.

For which positive integers k is the following series convergent. If K is bigger than two then the denominator has degree k which is also larger than to because youLL be multiplying K terms here. The objective is to find for which positive integers.

Sw Mong pe n1 kn. We have a n n 2 k n. For which positive integers k is the following series convergent.

E for which positive integers k is the following series convergent. Previous question Next question. Sum n1 -- infinity n 2 kn.

About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy Safety How YouTube works Test new features Press Copyright Contact us Creators. For a fixed positive integer consider the following series. An infinite sum of positive integers greater than 1 obviously is not convergent.

K 2 k 2 k 2. N 1 k. Hence k 2 the series converges by comparison test.

For which positive integers k is the following series convergent. Show activity on this post. Answer to For which positive integers k is the following series convergent.

Infinite n 1 n2kn. For which positive integers k is the series given below convergent. So K equals two will give convergence and similarly heres the key step here.

-1-102 Σ 13 n1 S. And one could use Lopezs house rule here to see that this living goes toe one over fourth which is less than one. Early Transcendentals 8th Edition James Stewart Chapter 116 Problem 44E.

When the series does NOT converge. 3 2 2 2 n 1 2 n 2. N1 4444420 Page 3 of 4 n2 kn.

2 π n n e 2 n 2 π k n k n e k n 2 π n k 1 k k n n e 2 k n. Texsum_n1inftyfracn2kntex the latex code is acting weird ill put it in regular text too. From the complete question the convergence of the series is calculated below.

Lim n n 1 2 2 n 1 2 n 2 1 4 limlimits_ n to infty dfrac n12 2n1 2n2 dfrac 1 4 n lim 2 n 1 2 n 2 n 1 2 4 1. The key to simplification of these expressions is recognizing that n 1 2 n 1 2 n 2 n - 1 2. Kn 1 kn.

For which positive integers k is the following series convergent. We have to find for which positive integers does this series converge. This answer is not useful.

Since we know that both k and n are positive we can omit absolute bars. For which positive integers k is the following series convergent. This answer is useful.

Step 1 of 4. So K equals two will give convergence and similarly heres the key step here. For which positive integers k is the following series convergent.

We have step-by-step solutions. Step 1 of 4. Similarly k n 1.

For a fixed positive integer consider the following series. Solution for For which positive integers k is the following series convergent. Lim n 1² kn 1 lim n 1k Therefore the series will be convergent if k 2n since.

Textbook solution for Single Variable Calculus. N 1 - 27249629.

Solved For Which Positive Integers K Is The Following Series Chegg Com

For Which Positive Integers Of K Is Series Convergent N Kn Youtube

Solved For Which Positive Integers K Is The Following Series Chegg Com