Answers

1. Since |12/11|>1, the given series is a divergent series.

   What is convergent and divergent series?

   • n=112n=12+14+18+116+ is a simple example of a convergent series.
   • The partial sums are 12,34,78,1516, and we can see that they are getting closer to 1.
   • The first partial sum is 12 away, the second 14 away, and so on until it approaches 1 infinity.

   • A divergent series is an infinite series that is not convergent, which means that the infinite sequence of the series partial sums has no finite limit.
   • Nicole Oresme, a medieval mathematician, demonstrated the divergence of the harmonic series.

   To determine whether the playlist is convergent or divergent:

   Given –  

   ∞

   ∑ (1+12ⁿ/11ⁿ)

   ⁿ⁻¹

   As, general form is A+B/C = A/C + B/C.

   So,

   • = ∑ (1/11ⁿ + 12ⁿ/11ⁿ)
   • = ∑1/11ⁿ + ∑(12/11)ⁿ
   • = ∑(1/11)ⁿ + ∑(12/11)ⁿ
   • = ∑(1/11)¹(1/11)ⁿ⁻¹ +  ∑12/11(12/11)ⁿ⁻¹
   • So, ∑ a·rⁿ⁻¹    if |r|<1   →    Convergent.
   • Then |1/11|<1 (convergent) and  |12/11|>1 (divergent)
   • Since |12/11|>1, the series is divergent.

   Therefore, the given series is a divergent series.

   Know more about convergent series here:

   https://brainly.com/question/337693

   #SPJ4

   The correct question is given below:

   Determine whether the playlist is convergent or divergent.

   ∞

   ∑ (1+12ⁿ/11ⁿ)

   ⁿ⁻¹

   Reply