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Examples of Sequence Convergence and Divergence

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Explanations 1

For an example of a convergent sequence, let us examine an=(1+1n)na_n = \left(1 + \dfrac{1}{n}\right)^nan=(1+n1)n, the well known sequence that converges to eee, Euler's numbe…
By Water Those, Cameron Montag, Alex Federspiel

Problems 3

How does the harmonic series ∑n=1∞1n\displaystyle \sum_{n=1}^{\infty}\frac{1}{n}n=1∑∞n1 behave?
Consider the infinite sequence defined by an=1na_n = \frac{1}{n}an=n1 . Is this sequence convergent?
How does the following series behave? ∑n=0∞xn\sum_{n=0}^\infty x^nn=0∑∞xn