Express the sum as a p-series.
∞n=1( 2^-ln(n)) (Hint: 2−ln(n) = 1/n^ln2)
Identify p
p=?
Express the sum as a p-series. ∞n=1( 2^-ln(n)) (Hint: 2−ln(n) = 1/n^ln2) Identify p p=?
Express Ln as a function of Fibonacci numbers: Hint: Guess the value of Ln (for small n) as a sum of some Fibonacci numbers Prove that your identity for Ln is correct for . Express Ln as a function of Fibonacci numbers: Hint: Guess the value of Ln (for small n) as a sum of some Fibonacci numbers Prove that your identity for Ln is correct for .
Find the values of p for which the series is convergent. ∞ 5 n(ln(n)) p n = 2 Find the values of p for which the series is convergent. sigma_n = 2^infinity 5/n(In(n))^p p >
1. Express the sum m-1 k-0 in closed form. [Hint: The sum is a finite geometric series.] 2. Find the equation of the line connecting the endpoints of the graph of sin(x) on the interval [0, π/2] 1. Express the sum m-1 k-0 in closed form. [Hint: The sum is a finite geometric series.] 2. Find the equation of the line connecting the endpoints of the graph of sin(x) on the interval [0, π/2]
Problem 3. Consider the series: 1 n [ln (n)]4 n=2 a) (6 pts) Use the integral test to show that the above series is convergent. b) (4 pts) How many terms do we need to add to approximate the sum within Error < 0.0004.
Euler found the sum of the p-series with p = 4: (4) = infinity n = 1 1/n^4 = pi^4/90 Use Euler's result to find the sum of the series. Infinity n = 1 (3/n)^4 81/90 pi^4 infinity k = 6 1/(k - 3)^4
Which of the following series converges conditionally? ono (-1)n-1 n=1 2 + ln(n) § 4-3)* 1-7) non
Euler found the sum of the p-series with p = 4: Use Euler's result to find the sum of the series Euler found the sum of the p-series with p = 4: 1 ga) = n4 90 n=1 Use Euler's result to find the sum of the series. 314 n=1 (k - 1)4 k=4
(1 point) Express the following sum in closed form /2 Σ (342k) k-l Hint: Start by multiplying out (32k)2. Note: Your answer should be in terms of n.
(In2)2 +1 -2 sin r+ (In 2)2 cos x Evaluate /2 cos z da In 2 2° cos x + 2° sin (In 2) ln 2 1 +ln2 ln2 (In 2) (In2)2 +1 -2 sin r+ (In 2)2 cos x Evaluate /2 cos z da In 2 2° cos x + 2° sin (In 2) ln 2 1 +ln2 ln2 (In 2)
Question 8 n²+2 The series (-1)" (n3 + 5)ln n is n=1 Absolutely Convergent Conditionally Convergent Divergent Cannot Be Determined Show or upload your work below. Edit Insert Formats В І ox, x A E :