Math Problem Statement
Use the formula S
=StartFraction n left parenthesis n plus 1 right parenthesis Over 2 EndFractionn(n + 1)2
to find the sum of 1 + 2 + 3 + ... +
Question content area bottom
Part 1
1 + 2 + 3 + ... +
970970
= enter your response here
Solution
To find the sum of the series , we can use the formula .
Here, .
Let's calculate the sum:
So, the sum is .
Would you like further details or have any questions?
Here are 5 related questions:
- How would the sum change if the series went up to 1000 instead of 970?
- What is the sum of the first 500 natural numbers?
- How does the sum formula change if you sum from 2 to 970 instead of 1 to 970?
- Can this method be used for summing negative integers?
- How would you find the sum of the first odd numbers?
Tip: When calculating large sums, ensure you carefully handle multiplication and division to avoid errors, especially when is large.
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Math Problem Analysis
Mathematical Concepts
Series sum
Arithmetic progression
Formulas
Sum formula of arithmetic series: S = n(n + 1) / 2
Theorems
-
Suitable Grade Level
Grades 7-9