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 1+2+3++9701 + 2 + 3 + \dots + 970, we can use the formula S=n(n+1)2S = \frac{n(n+1)}{2}.

Here, n=970n = 970.

Let's calculate the sum:

S=970(970+1)2S = \frac{970(970 + 1)}{2}

S=970×9712S = \frac{970 \times 971}{2}

S=9418702S = \frac{941870}{2}

S=470935S = 470935

So, the sum 1+2+3++9701 + 2 + 3 + \dots + 970 is 470,935470,935.

Would you like further details or have any questions?

Here are 5 related questions:

  1. How would the sum change if the series went up to 1000 instead of 970?
  2. What is the sum of the first 500 natural numbers?
  3. How does the sum formula change if you sum from 2 to 970 instead of 1 to 970?
  4. Can this method be used for summing negative integers?
  5. How would you find the sum of the first nn odd numbers?

Tip: When calculating large sums, ensure you carefully handle multiplication and division to avoid errors, especially when nn 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

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Suitable Grade Level

Grades 7-9