Respuesta :
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
