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(a) Use Bounded Monotonic Sequence Theorem to show that the sequence with the given nth term...
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an
3. Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find the limit. (a)a, = 1+(-1)"+1 (b) a, = sian
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, entee DIVERGES.) [-/1 Points] DETAILS LARCA Determine the convergence or diverge (n − 2)! n! an Need Help? Read It Talk to
In questions 1-8, find the limit of the sequence. sin n cos n 2. 37 /n sin n 3. 4. cos rn 5. /n sin n o cos n n! 9. If c is a positive real number and lan) is a sequence such that for all integer n > 0, prove that limn →00 (an)/n-0. 10. If a > 0, prove that limn+ (sin n)/n 0 Theorem 6.9 Suppose that the sequence lan) is monotonic. Then ta, only if...
5 Consider the following continued fraction 2 + (i) Write the above continued fraction as the limit of a sequence. Also write a recurrence relation between the terms of the sequence. (ii) Show that the sequence is bounded. (i) Show that the subsequence of odd-indexed terms and even-indexed terms are monotonic. (iv) Show that the above continued fraction converges and find the limit. 5 Consider the following continued fraction 2 + (i) Write the above continued fraction as the limit...
Question 8 Use the nth-Term Test for divergence to show that the series is divergent, or state that the test is inconclusive. n1 inconclusive diverges converges, 6 converges. Question 9 Estimate the magnitude of the error involved in using the sum of the first four terms to approximate the sum of the entire series. 5-19*loze Error 107 10 no 400 * 10" Error 6.40*10 Error 3.20 x 10
6. Given an n21 2n+3) a) Is the sequence monotonic? b) Is the sequence bounded? c) Does the sequence converge or diverger
1 please 1. Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limita T1-2nt
please do both question clearly,thank you! Consider the sequence of real numbers 13. 1 1 2' 1 2 + 2 + 1 2 + Show that this sequence is convergent and find its limit by first showing that the two sequences of alternate terms are monotonic and finding their limits. Prove that any sequence in hence we may suppose that each subsequence has a least term.) (Note that this result and the theorem on the convergence of bounded monotonic sequences...
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a, and common difference, d Find a1so when a,-50, d-5 a1s0"