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sum of numbers 1 to 50

Understand the Problem

The question is asking for the sum of all whole numbers from 1 to 50. To solve this, we can use the formula for the sum of an arithmetic series or simply add the numbers sequentially.

Answer

The sum is $1275$.
Answer for screen readers

The sum of all whole numbers from 1 to 50 is $1275$.

Steps to Solve

  1. Identify the first and last numbers in the series

The first whole number in your series is 1 and the last whole number is 50.

  1. Use the sum formula for an arithmetic series

The formula for the sum ( S ) of the first ( n ) whole numbers is given by:

$$ S = \frac{n(n + 1)}{2} $$

Here, ( n ) is the last number in the series, which is 50.

  1. Plug the value into the formula

Substituting ( n = 50 ) into the formula:

$$ S = \frac{50(50 + 1)}{2} $$

  1. Calculate the sum

Now calculate:

$$ S = \frac{50 \cdot 51}{2} $$

This simplifies to:

$$ S = \frac{2550}{2} $$

  1. Finalize the answer

So,

$$ S = 1275 $$

The sum of all whole numbers from 1 to 50 is $1275$.

More Information

The formula used, ( S = \frac{n(n + 1)}{2} ), is a well-known shortcut for calculating the sum of the first ( n ) natural numbers and allows for quick calculations without needing to manually add each individual number.

Tips

  • Forgetting the division by 2 in the formula, which can lead to doubling the sum.
  • Miscalculating ( n(n + 1) ) before dividing, which may result from overlooking the order of operations.
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