Which of the series E=1a, defined by the formulas in Exercises 5–8 converge, and which diverge? Give reasons for your answers. n(n + 1) 5. а, — 1, ал+1 (n + 2)(n + 3)ªn (Hint: Write out several terms, see which factors cancel, and then generalize.) п 6. ај — аз —D 7, а,+1 (n – 1)(n + 1)' a, if n > 2 7. a¡ = a2 = 1, a„+1 = if n 2 2 1 + an 8. a, = 1/3" if n is odd, a, = n/3" if n is even

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