Question

Let (a) Determine whether {a} is convergent. convergent divergent (b) Determine whether is convergent. convergent divergent

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:
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The correct question is given below:
Determine whether the playlist is convergent or divergent.
∑ (1+12ⁿ/11ⁿ)
ⁿ⁻¹