To write the sum \(1 + 2 + 3 + ... + 10\) using sigma notation:
The sequence starts at \(i = 1\) and ends at \(i = 10\). Each term in this sequence is simply \(i\). Therefore, we can express this sum as:
\[\sum _ { i= 1} ^ { 10} i\]
This compact form effectively represents adding all integers from 1 through 10.
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Supplemental Knowledge

Summation notation, also known as sigma notation, is a compact way to represent the sum of a sequence of terms. The Greek letter sigma (\(\Sigma \)) is used to denote the sum. The general form of summation notation is:
\[\sum _ { i= a} ^ { b} f( i) \]
where:

• \(i\) is the index of summation.
• \(a\) is the lower limit of summation (the starting value).
• \(b\) is the upper limit of summation (the ending value).
• \(f( i) \) represents the function or expression to be summed.
  For example, to write the sum of integers from 1 to 10 using sigma notation, we use:
  \[\sum _ { i= 1} ^ { 10} i\]
  This represents the sum \(1 + 2 + 3 + ... + 10\).

Life in Context

Summation notation has long been used in various disciplines like statistics, computer science and physics. For instance, in statistics it can help calculate the mean or variance of data sets by adding all its points together; similarly computer scientists often rely on summation notation algorithms that involve adding up sequences of numbers, for tasks like running total calculations or time complexity analysis.

Mastering concepts like series and summation notation can significantly enhance your mathematical abilities and analytical skills. At UpStudy, we provide comprehensive resources that cover algebra and other mathematical topics in depth. Whether you're preparing for exams or looking to deepen your understanding, explore UpStudy’s live tutor question bank or our AI-powered problem-solving services for detailed insights.
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