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Summation Notation

Concept

Summation Notation

The summation notation, also known as sigma notation, allows long sums to be written in a compact way. It is denoted using the Greek letter sigma along with several other pieces of information about the summation.

The variable is called the summation index and only takes integer values. To write this sum explicitly, the variable appearing after sigma must be substituted with the integers from the initial value through the last value. Notice some aspects of summation notation:

  • The summation does not depend on the summation index used.
  • Sometimes a summation may involve other variables. These should not be confused with the summation index. Here, the summation index is Therefore, the indicated values should only be substituted into and not into
  • The initial value can be any integer less than or equal to the number above the summation symbol. The number above only indicates the final value needed to be substituted for not the number of terms.

The summation notation is not only useful for working with sums involving a large number of terms, but it can also be used to represent an infinite sum.