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please answer both of them with clear writing. # Without using P-Series rule, prove that ih...
State and prove divergence or convergence for each of the
following Series.
(please answer all of them in clear writing)
a. 3" Vn cos(ien) b. Å vn cos n+1 n=1 c. Ën+2 n+2 nn n=1 2" n! d. 11 n=1 3"n! e. 12
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prove and compute the questions with clear hand writing.
I need to understand clearly, so when you prove these questions,
please prove it step by step clearly!!!!
3- Let f: [0,1R be defined by f(x) = x2. For each n e N, let P be the partition of [0, 1 into n equal subintervals 3-1) Find formulas for U (f, P,) and L(f, P,). You may use the formula 2 = " n)without proof....
PLEASE ANSWER ALL! SHOWS STEPS
2. (a) Prove by using the definition of convergence only, without using limit theo- (b) Prove by using the definition of continuity, or by using the є_ó property, that 3. Let f be a twice differentiable function defined on the closed interval [0, 1]. Suppose rems, that if (S) is a sequence converging to s, then lim, 10 2 f (x) is a continuous function on R r,s,t e [0,1] are defined so that r...
Please prove why this series diverges!
3 n2 - 2 (sum does not converge) n=1 4n25 +n
Please do both questions.
Q5 (5 points) Using the comparison test, determine if the series 2” vn +1 converges or diverges. n n=1 Q6 (5 points) 00 n Using the comparison test, determine if the series converges or diverges. n3 +n +3 n=1
please answer 3 of the question in clear writing.
Find the radius and interval of convergence of the following power series. a. b. Σ (x + 1)" C. Σ(-1): (x-2)" n? 3"
please answer questions with details and clear steps
and clear hand writing (8,9,10,11
S. Find the values of p for which the series is convergent. /2 9. Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded? a s " 2n +3 10. Test the series for convergence or divergence. 72 11. a) Use the integral test to show that the series converges In+1 b) Find s,o c) Use the error bounds from the integral...
Please answer both parts and label them clearly
Let p denote the population proportion. Provided that sample size n is large, let p be the sample proportion unknown. 1. At significance level of a, find the rejection region (decision rule) for the following hypotheses. Ho : p= Po, H :p> po. 2. For the rejection region (decision rule) in (1) find the 8 when p = pi (p)).
The sum diverges. Use the limit test to prove it.
Determine if the series is convergent or divergent. If the series is absolutely convergent, note that in the summary. For the summary: 1. Clearly indicate which test you are using. 2. Verify that the series meets the requirements for that test. 3. Clearly summarize the results of the test. (n!)" 2 nan n=1
please answer a through f
5. For the following series, find the sum of the series or determine that it diverges. 2n 7 n=0 n=0 (-2)n+1 n² n 3n2 + n-1 9 (f) L 3n n=0