Agree or Disagree with each of the following statements? Statement 1: Let 2 an and 2 b, be 2 divergent series, then the series 2 (á, + bn) is also a divergent series. n=1 n=1 n=1 Statement 2: Let 2 a, be a convergent series and 2 bn be a divergent series, then the series 2 (a, + b,) is a divergent series. n=1 n=1 n=1 If you agree, explain (mathematically) why. If you disagree, give an example to show why the statement is incorrect.

Q: The sum of the series (if it exist) is Ln=1 +11n+30

A: Given, ∑n=1∞1n2+11n+30 To evaluate sum of series if it exists

Q: 00 с 1. Š (1)"(nº +1) en n=1

A: As per our norms .we have to answer. One question at a time.. kindly repost remaining questions

Q: Let {an}o be a sequence with positive terms. (a) Prove that if lim van= ∞, then La, diverges. (b)…

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Q: If a given series converges and each term is positive, then the square of the series also converges.

A: The statement is true.

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A: To prove the given statement using the comparison test.

Q: The great Swiss mathematician Leonhard Euler sometimes reached incorrect conclusions in his…

A:

Q: 5. Use Theorem 5.10 (Section 5.3 in Vol. 2 of OpenStax Calculus) for this problem. How many terms of…

A:

Q: 2n-3 00 Ση=1 5n+4

A: If limn→∞(∑n=0∞an)=L, where L= Number other than zero, then ∑n=0∞an divergesIf limn→∞(∑n=0∞an)=0,…

Q: )  Suppose that ∞     n = 1an = 1, that ∞     n = 1bn = −1, that a1 = 2,

A:

Q: 8. Consider the geometric series En=1 the third term az = 12. Which of the following statements…

A: Geometric series.

Q: 2).  For an as follows, write the sum        an as a geometric series. a1 =  1 14 and  an an + 1

A: This is a question of infinite series.

Q: 17. For a geometric series, What are the first three terms of the series if the first term is 3? 17

A: