My Math Forum

My Math Forum (http://mymathforum.com/math-forums.php)
-   Elementary Math (http://mymathforum.com/elementary-math/)
-   -   Suite 1 2 10 11 12 13..n (http://mymathforum.com/elementary-math/345823-suite-1-2-10-11-12-13-n.html)

Zou37 February 20th, 2019 02:35 AM

Suite 1 2 10 11 12 13..n
 
Hello everyone,

I am looking to calculate the sum Sn = 1 + 2 + 10 + 11 + 12 + 13 + 14 .... n
According to n
And calculate n according to Sn.

v8archie February 20th, 2019 02:59 AM

If you mean $$S_n = (1 + 2 + 3 + \ldots + n) - (3 + 4 + 5 + 6 +7+8+9)$$ the first bracket has a well-known closed form in terms of $n$ and the second is a constant.

Zou37 February 20th, 2019 03:07 AM

can that be done?
because in a toy with infinite sums.

Denis February 20th, 2019 05:46 AM

Quote:

Originally Posted by Zou37 (Post 606064)

I am looking to calculate the sum Sn = 1 + 2 + 10 + 11 + 12 + 13 + 14 .... n

Example:
1 + 2 + 10 + 11 + 12 = 36
a = 10, d = 1, n = 5
Formula:
3 + {(n-2)*[2*a + d*(n - 3)]}/2

Tu comprends?

Zou37 February 20th, 2019 09:01 AM

Quote:

Originally Posted by Denis (Post 606071)
Example:
1 + 2 + 10 + 11 + 12 = 36
a = 10, d = 1, n = 5
Formula:
3 + {(n-2)*[2*a + d*(n - 3)]}/2

Tu comprends?

No .

Denis February 20th, 2019 09:14 AM

Quote:

Originally Posted by Denis (Post 606071)
Example:
1 + 2 + 10 + 11 + 12 = 36
a = 10, d = 1, n = 5
Formula:
3 + {(n-2)*[2*a + d*(n - 3)]}/2

3 + {(n-2)*[2*a + d*(n - 3)]}/2
3 + {(5-2)*[2*10 + 1*(5 - 3)]}/2 = 36

WHAT do you not understand?

The regular arithmetic series is 10 + 11 + 12 .....
What appears before the regular series is 1 + 2
So solve the regular series, then add the
irregular portion which is 1+2 = 3

If you're not sure of the formula, google "arithmetic series".

C'est bon?

EDIT:
note that if a = d = 1, then you have consecutive natural numbers,
so formula can be condensed to n(n + 1)/2; example:
1 + 2 + 3 + 4 + 5 = 15
5*6 / 2 = 15
Those are known as triangular numbers;
for above example: 5th triangular number = 15

Zou37 February 20th, 2019 09:25 AM

3+infini=10+infini=.... car (10+11+12+....=infini)

skipjack February 20th, 2019 09:48 AM

You wanted to calculate the sum "according to n", where n is an integer greater than 9. This can't be infinite.

Sn = 3 + (n - 9)(10 + n)/2 = (n² + n - 84)/2

Zou37 February 20th, 2019 10:06 AM

Quote:

Originally Posted by skipjack (Post 606076)
You wanted to calculate the sum "according to n", where n is an integer greater than 9. This can't be infinite.

Sn = 3 + (n - 9)(10 + n)/2 = (n² + n - 84)/2

U0=1
U1=2
n>=3 Un=7+n

Here Sn=(n^2+15n)/2-14

n>=0 Sn=????

skipjack February 20th, 2019 10:12 AM

You didn't state originally that n is the number of terms. Why define Un? There is no Un in the question or in your solution.


All times are GMT -8. The time now is 04:51 AM.

Copyright © 2019 My Math Forum. All rights reserved.