Prove:
without using l'hopital's rule.
Prove: without using l'hopital's rule. infinity 2n-1 ln(2) (2n-1) n infinity 2n-1 ln(2) (2n-1) n
Consider the sequence: {an = ln (2n? +n) – In(n? +10)}. (1) Give a, and a2 (2) Find algebraically (without using a calculator) the limit of the sequence if it exists. Show your work.
a.) Use L'Hopital's Rule to evaluate [Hint: Consider ln L.] b) Determine the convergence of L = lim (1--)r We were unable to transcribe this image
Determine if the series convergence or divergence and state the test used: # 1.) sigma on top infinity when n=1 [(5/2n-1)] # 2.) sigma on top infinity when n=1 [(2 * 4 * 6 …2n/n!)]
Prove that P2n(0)= (-1)n ((2n-1)!!/(2n)!!) using the generation function and a binomial expansion. Show that (sqrt(pi)(4n-1)/(2gamma(n+1)gamma(3/2-n))=(-1)n-1((2n-3)!!/(2n-2)!!)(4n-1)/2n
Evaluate the limit using techniques from Chapters 1 and 3 and using L'Hopital's Rule. lim x→−3 5x2 + 1x − 42 x + 3 (a) using techniques from Chapters 1 and 3 (b) using L'Hopital's Rule
By using a constructive method, prove that there is a positive integer n such that n! < 2n By using an exhaustive method, prove that for each n in [1.3], nk 2n. By using a direct method, prove that for every odd integer n, n2 is odd. By using a contrapositive method, prove that for every even integer n, n2 By using a constructive method, prove that there is a positive integer n such that n!
1. Prove that 1.3....2n-1 1. Prove that-.-. ...--ㄑㄧ for any n E N 2n V2n+1
Use series representation(s) to evaluate the following limit (You may not use L'Hopital's rule). . X – 1 (Hint : ln(x) = ln(1 + (x – 1)]). x+1 ln(x) lim
2n 3. Prove that lim n+on+ 1 2.
Determine whether the sequence an = ln(2n + 1) - In(n +2) converges or diverges, and if it converges, find the limit. Find the length of the curve defined by x = 2t3, y = 3t2, osts 1.