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

Answers

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.

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