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Summation notation

We can describe sums with multiple terms using the sigma operator, Σ. Learn how to evaluate sums written this way.
Summation notation (or sigma notation) allows us to write a long sum in a single expression.

Unpacking the meaning of summation notation

This is the sigma symbol: . It tells us that we are summing something.
Let's start with a basic example:
Stop at n=3(inclusive)n=132n1Expression for eachStart at n=1term in the sum
This is a summation of the expression 2n1 for integer values of n from 1 to 3:
Notice how we substituted n=1, n=2, and n=3 into 2n1 and summed the resulting terms.
n is our summation index. When we evaluate a summation expression, we keep substituting different values for our index.
Problem 1
صرف 1 جواب چنو

We can start and end the summation at any value of n. For example, this sum takes integer values of n from 4 to 6:
We can use any letter we want for our index. For example, this expression has i for its index:
Problem 2
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Problem 3
Consider the sum 4+25+64+121.
Which expression is equal to the above sum?
Choose all answers that apply: وہ سب سلیکٹ کریں جو مناسب ہے

Some summation expressions have variables other than the index. Consider this sum:
Notice that our index is n, not k. This means we substitute the values into n, and k remains unknown:
Key takeaway: Before evaluating a sum in summation notation, always make sure you identified the index, and that you are only substituting into that index. Other unknowns should remain as they are.
Problem 4
صرف 1 جواب چنو

Want more practice? Try this exercise.