A) telescopic series B)divergent geometric series C)divergent p series D)converg

Question

A) telescopic series B)divergent geometric series C)divergent p series D)convergent p series E)converges by comparison with 1/n^3 F)An converges G)diverges by the nth term H)1/n^2 + 1 converges I)An diverges J)convergent geometric series 1. lim nt2 2. lim'/lanl =- 3.12 4. 5. n410 a. Serie telescópica b. Serie geométrica divergente c. Serie-p divergente d. Serie-p convergente e·Converge por comparación con an 71 371 rt 10n+1 an converge 2n 8. Diverge por enésimo término h. nl converge i, an diverge j. Serie geométrica convergente 7t n2-10 8, 2.an5 n2+i n n+1 10.fo.2+1 dx

Explanation / Answer

1-G)diverges by the nth term(by ratio test)

2-F)An converges( cauchy nth root test)

3-B)divergent geometric series (by geometric test)

4- C)divergent p series (by p test or auxiliary test)   

5-I)An diverges (by comparison test)

6-J)convergent geometric series (by geometric test)

7- D)convergent p series (by p test or auxiliary test)

8- E)converges by comparison with 1/n^3 (by comparison test)

9- A) telescopic series (by expansion, the limit of the nth term is 1(fixed number) as n tends to infinity)

10- H)1/n^2 + 1 converges (by Integral test)

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