Summing Consecutive Integers

[greatwhiteshark]

The sum of the consecutive integers 1,2,3....n, is given by the formula
1/2 times n(n + 1). How many consecutive integers, starting with 1, must be added to get a sum of 666?

 

[pka]

165+166+167+168

 

[Gene]

Cute :!: And correct, they do begin with 1.
n(n+1)=2*666=1332
n^2+n-1332=0

 

[pka]

I don’t think that it is CUTE!
Look 197+198+199=594.
So it is going to take four.
196+197+198+199=790.
(790-666)/4 = 31.
Thus 196-31=165; 165+166+167+168=666.
That is the way a mathematician thinks.

 

[Gene]

To pka:
I said CUTE and correct. Lewis Carol and Alice would both be proud of you.
If Janet had said what I think she meant, "Starting with 1, how many consecutive integers must be added to get a sum of 666?" could you play that trick with the English language?
A mathematician thinks every cat has ten tails.
(No cat has nine tails.
Every cat has one more tail than no cat.
QED
Forget about Manx cats!)
-----------------
Gene

 

[Denis]

ya'll wrong! 1332 is answer:

-665, -664, .... -1, 0, 1, ... 664, 665, 666

 

[Denis]

The sum of the consecutive integers 1,2,3....n, is given by the formula
1/2 times n(n + 1). How many consecutive integers, starting with 1, must be added to get a sum of 666?

Ok, to get serious...

1/2 times n(n + 1) is same as n(n + 1) / 2

Taking a simple example: 1 + 2 + 3 + 4 + 5 = 15
And 5(5 + 1) / 2 = 5(6) / 2 = 30 / 2 = 15

So if question is: how many consecutive integers from 1 add up to 15?
Then: n(n + 1) / 2 = 15
n(n + 1) = 30
n^2 + n - 30 = 0
(n+ 6)(n - 5) = 0
n = -6 or n = 5 : -6 is impossible, so answer is 5 : ok, Janet?

Now do 666 that way...you should get same equation as Gene's first post