How do you find the sum of an infinite series?

Answer 1

By definition this is #sum_(i=0)^oo a_i = lim_(n->oo)sum_(i=0)^n a_i#. So just calculate the sum from zero to #n# and then take the limit where #n# approaches infinity.

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Answer 2

Evelyn Agard

To find the sum of an infinite series, we use various techniques such as arithmetic series, geometric series, or other specialized methods like telescoping series or the ratio test. Each series has its own method of finding the sum, which may involve finding a closed-form expression, determining convergence or divergence, or utilizing known mathematical properties. It's essential to identify the type of series and apply the appropriate method to find its sum accurately.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.