1+2+3+...+230
Use the method of Gauss to find the sum
To find the sum of the sequence 1+2+3+...+230, we can use the method of Gauss.
The formula to find the sum of an arithmetic series is given by:
Sum = (n/2)(first term + last term)
In this case, the first term (a) is 1 and the last term (l) is 230.
Using the formula, we have:
Sum = (230/2)(1 + 230)
= 115(231)
= 26565
Therefore, the sum of the sequence 1+2+3+...+230 is 26,565.
To find the sum of the series 1 + 2 + 3 + ... + 230 using the method of Gauss, we can employ the formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is given by:
Sn = (n/2)(a + L)
where:
- Sn is the sum of the series
- n is the number of terms in the series
- a is the first term of the series
- L is the last term of the series
In this case:
- n = 230 (the number of terms)
- a = 1 (the first term)
- L = 230 (the last term)
Thus, substituting the values into the formula, we have:
Sn = (230/2)(1 + 230)
= (115)(231)
= 26,565
Therefore, the sum of the series 1 + 2 + 3 + ... + 230 is 26,565.
To find the sum of the numbers from 1 to 230, we can use the method known as Gauss summation. This method involves finding the sum of the first and last numbers in the sequence, and then multiplying it by the number of terms and dividing by 2.
In this case, we can find the sum by applying the formula:
Sum = (first number + last number) * (number of terms) / 2
The first number is 1 and the last number is 230. The number of terms can be calculated by subtracting the first number from the last number and adding 1 (since we're counting every number between them).
So, the number of terms = 230 - 1 + 1 = 230.
Now, let's plug these values into the formula:
Sum = (1 + 230) * (230) / 2
Simplifying further:
Sum = 231 * 230 / 2.
To compute this expression, divide 231 by 2, and then multiply the result by 230:
Sum = 115.5 * 230
Finally, calculating the result:
Sum = 26,595.
Therefore, the sum of the numbers from 1 to 230 is 26,595.