Question
The sum of a sequence of consecutive numbers from 1 to n is given by the formulia n(n+1)/2
Answers
GPT-4o mini
Yes, that's correct! The sum of a sequence of consecutive numbers from 1 to \( n \) can be calculated using the formula:
\[
S = \frac{n(n + 1)}{2}
\]
where \( S \) is the sum and \( n \) is the last number in the sequence. This formula works because it effectively pairs numbers in the sequence to simplify the addition. For example, when you write the numbers down in pairs from the start and end, each pair sums to the same value:
1. For \( n = 1 \): \( S = \frac{1(1+1)}{2} = 1 \)
2. For \( n = 2 \): \( S = \frac{2(2+1)}{2} = 3 \)
3. For \( n = 3 \): \( S = \frac{3(3+1)}{2} = 6 \)
4. For \( n = 4 \): \( S = \frac{4(4+1)}{2} = 10 \)
And so on. This formula is very useful in various mathematical problems and can also be applied in programming for efficient computation of sums of consecutive integers.
\[
S = \frac{n(n + 1)}{2}
\]
where \( S \) is the sum and \( n \) is the last number in the sequence. This formula works because it effectively pairs numbers in the sequence to simplify the addition. For example, when you write the numbers down in pairs from the start and end, each pair sums to the same value:
1. For \( n = 1 \): \( S = \frac{1(1+1)}{2} = 1 \)
2. For \( n = 2 \): \( S = \frac{2(2+1)}{2} = 3 \)
3. For \( n = 3 \): \( S = \frac{3(3+1)}{2} = 6 \)
4. For \( n = 4 \): \( S = \frac{4(4+1)}{2} = 10 \)
And so on. This formula is very useful in various mathematical problems and can also be applied in programming for efficient computation of sums of consecutive integers.