Math Problem Statement

Evaluate the sum from i = 1 to i = 2 of the expression 5 + 3i: \(\sum_{i=1}^{2} (5 + 3i)\)

Solution

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Test for Quiz:

Evaluate the sum from i=1i = 1 to i=2i = 2 of the expression 5+3i5 + 3i:

i=12(5+3i)\sum_{i=1}^{2} (5 + 3i)


To solve this summation:

  1. Plug in the values of ii into the expression:

    • For i=1i = 1: 5+3(1)=5+3=85 + 3(1) = 5 + 3 = 8
    • For i=2i = 2: 5+3(2)=5+6=115 + 3(2) = 5 + 6 = 11
  2. Add the results: 8+11=198 + 11 = 19

So, the sum i=12(5+3i)\sum_{i=1}^{2} (5 + 3i) is 19.

Would you like more details on this problem, or do you have any questions?

Here are five related questions you might find interesting:

  1. How do you compute a summation with more terms, say from i=1i = 1 to i=5i = 5?
  2. What is the general formula for the sum of an arithmetic series?
  3. How does summation notation apply to functions other than linear ones?
  4. Can you calculate the sum of a geometric series using a similar method?
  5. How would the sum change if the expression inside the summation were a quadratic equation?

Tip: When working with summations, always break down the expression step by step and calculate each term individually before adding them together.

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Math Problem Analysis

Mathematical Concepts

Summation
Arithmetic Sequences

Formulas

Sum of an arithmetic sequence \(\sum_{i=1}^{n} (a + bi)\)

Theorems

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Suitable Grade Level

Grades 9-10