(2). you are given the fallawing series: n' 24 what is the suallest of termus thont to be odded to estimate with an less than o1 ! num ber wou ld have or oler its sum in absalu te error th at is o1?

Q: 1. Consider the power series 27² 2"n n=1 a. Write the first three nonzero terms of the power series.…

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Q: For the discrete series given as, X variable values - 32 with frequemcy 2, 37 with frequency 5, 46…

A: Solution-: We given the discrete series of values - 32 with frequency 2 37 with frequency 5 46 with…

Q: Considel the senes E3IJQA1P05 D7E3IJQA1P05 D7E3IJQA (-1)"+1 4 (n + 2)° Let Sy denote the partial sum…

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Q: IT Suppose that a, 3 10, а, 3D9, аз —8 a2 = 9, az =8 and that Σ. an= 2021. %3D n=1 Determine the…

A: We have to find

Q: For the discrete series given as, X variable values - 32 with frequemcy 2, 37 with frequency 5, 46…

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Q: E. Show that for 0 < p < 1, we have that Ep(1 – p)ª = 1. Hint: Remember the geometric series x=0…

A: GivenX~gem(p)P(X=x)=p(1-p)x    ; x=0,1,2,3,....we want to prove that ∑x=0∞p(1-p)x=1

Q: If a, = Elog,a', a>0,Find a,. Also findhow many terms %3D r=1 r=1 of the series aretobetakensothat…

A: We will find out the required values.

Q: 6. By expanding cosx using Maclaurin's series up to the first 3 non-zero terms, () evaluate cos

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Q: 27. 00 [ Given the series =0 12sin (+) 5²³-6 accurate to 4 decimal places? A. 37 terms B. 30 terms…

A: Number of terms required for approximation

Q: Use power series to estimate arctan .2 correct within -10-. Leave your answer as a simple fraction…

A: The power series for arctanx is x-x33+x55-x77+..... For a estimate within 12·10-5, we'll have to…

Q: 4. Consider the 2nd to 5th entries of the following two sequences and answer the questions be- low:…

A: D-Alembert's test: Let un is a sequence .…

Q: The value of p for the series En=1n! e¯n by using ratio test is 2 O 8.

A: Ratio Test: Let ∑n=1∞un be a given series such that limn→∞un+1un=ρ Then the series converges iff…

Q: Using power series, find a 5th degree polynonal.approximation to the solution'to the Inital alue…

A: Given a second order differential equation:- x2+1y''+y'+x-1y=0 To find the 5th degree polynomial…

Q: What is the sum of the series below if c = 4.5, d = 11.7, and x = 0.3. 26) n=0

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Q: 2- Show that the Sequence An define by and dn=Vant 2 for 'nI %3D is a monotonic increasing. a

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Q: 33. Find the Maclaurin series for e-, and use it to approx- 1 to within 0.001 of its value. How many…

A: Solution Given Find the Maclaurin series for e-x , and use it approximate 1/root e to with in 0.001…

Q: What is the sum of the following series? (n+2)2"-1 5n Lütfen birini seçin: 225 а. 32 b. 2 32 O c.…

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Q: Which table is a probability distribution table? X 1 P 0.4 X 1 P 0.4 X 1 P-0.2 X 1 P 0.2 2 0.15 2…

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Q: apopriate test to determine divergence" of the series. 7. Use He (onver gence DY ninta n= 00

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Q: Which of the following sequence is divergent? 3- 2n²\ n² + 1 S ( 3 sinh n sin n °{2(#)} 0{-3.} None…

A: Sol:- Check for Sequence Divergent Option :- First ∑n=0∞ 3-2n2n2+1Apply Series Divergence TestIf…

Q: 8. a. What is the power series reprsentation for centered at x = 0? Here, just %3D 1-x an answer is…

A: The power series expansion for fx=11-x is in the form ∑n=0∞xn That is: 1+x+x2+x3+........ Therefore,…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 6. A small metal bar, whose initial temperature was 20°C, is…

A: Given,Initial temperature is .Then,Then, by the formula of of Newton's law of heating we…

Q: X, suppose that the answer is desired 24. In computing the sum of an infinite series with an…

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Q: Use power series to approximate the definite integral, I, to six decimal places. *0.2 dx I =

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Q: 7. Uhe Hhe appopriate test to determine Conver gence divergence" of the series. DY nfn+2 n= 00

A: Given series is  ∑n=1∞1nn+2 where an=1nn+2