What is the formula for adding a sequence of consecutive numbers?

[shina]

Homework Statement

Homework Equations

The Attempt at a Solution

hey hello every one I want to ask a question that is add 1+2+3+4.....10000000. I think its very easy. for example let us add first 5 numbers 1+2+3+4+5 now we can find a pattern that adding first and last digit will be always same. for example 5+1=4+2 and similarly but it is a odd number that we can Ind easily by simple maths. so here we can multiply 6(addition of first and last number)×2(number of pairs) +3 because it is odd number

 

[shina]

Homework Statement

Homework Equations

The Attempt at a Solution

hey hello every one I want to ask a question that is add 1+2+3+4.....10000000. I think its very easy. for example let us add first 5 numbers 1+2+3+4+5 now we can find a pattern that adding first and last digit will be always same. for example 5+1=4+2 and similarly but it is a odd number that we can Ind easily by simple maths. so here we can multiply 6(addition of first and last number)×2(number of pairs) +3 because it is odd
number

I know I should write question separately but I couldn't

 

[phinds]

So what is your question? Is it simply "how do you add 1 + 2 + 3 + ... + n" ? If so, you need to show some attempt to do this yourself. HINT: it is trivially easy.

 

[fresh_42]

Homework Statement

Homework Equations

The Attempt at a Solution

hey hello every one I want to ask a question that is add 1+2+3+4.....10000000. I think its very easy. for example let us add first 5 numbers 1+2+3+4+5 now we can find a pattern that adding first and last digit will be always same. for example 5+1=4+2 and similarly but it is a odd number that we can Ind easily by simple maths. so here we can multiply 6(addition of first and last number)×2(number of pairs) +3 because it is odd number

The pairing of the greatest with the smallest number and working inwards looks fine.
Can you derive a formula for it, say 1+2+...+n for even n?
And for odd n, what happens if you apply your formula then on n-1 and add n separately?

 

[phinds]

Can you derive a formula for it, say 1+2+...+n for even n?

Yes. For ANY n. Try it. We don't spoon feed answers here, you have to show some work.

 

[Mayan Fung]

You may try to guess the formula by visualising the pattern. For example, draw one dot in the first line, two dots in the second, so on and so forth. Can you observe any pattern of the total number of dots?