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Definitions and notation

Sequence - a set of numbers in a certain order, e.g. ¹ ⁄ ₂, ¹ ⁄ ₄, ¹ ⁄ ₈, ¹ ⁄ ₁₆...

Term - each of the numbers above (e.g. ¹ ⁄ ₄) are a term of a sequence.

If a sequence is algebraic, each position can be denoted by a subscript, e.g. a₁, a₂, a₃, .... a_k.

Series - The result of all the terms of a sequence added together.

Summation - The process of adding all the terms together (indicated by ∑).

Limits - the first and last terms.

So a₁ + a₂ + a₃ + a₄ + a₅ can be written as ^k=5 ∑ _k=1 a_k or ⁵ ∑ _k=1 a_k or even more simpler ⁵ ∑ ₁ a_k.

If you're finding the summation, it can be written as ∑ _k a_k or even just ∑a_k.

Infinite Sequences - have an infinite number of terms.

Infinite Series - the summation of the infinite sequence.