February 20th, 2019, 02:35 AM  #1 
Banned Camp Joined: Feb 2019 From: France Posts: 8 Thanks: 0  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. 
February 20th, 2019, 02:59 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,663 Thanks: 2643 Math Focus: Mainly analysis and algebra 
If you mean $$S_n = (1 + 2 + 3 + \ldots + n)  (3 + 4 + 5 + 6 +7+8+9)$$ the first bracket has a wellknown closed form in terms of $n$ and the second is a constant.

February 20th, 2019, 03:07 AM  #3 
Banned Camp Joined: Feb 2019 From: France Posts: 8 Thanks: 0 
can that be done? because in a toy with infinite sums. 
February 20th, 2019, 05:46 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,588 Thanks: 1038  
February 20th, 2019, 09:01 AM  #5 
Banned Camp Joined: Feb 2019 From: France Posts: 8 Thanks: 0  
February 20th, 2019, 09:14 AM  #6  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,588 Thanks: 1038  Quote:
3 + {(52)*[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 Last edited by Denis; February 20th, 2019 at 09:28 AM.  
February 20th, 2019, 09:25 AM  #7 
Banned Camp Joined: Feb 2019 From: France Posts: 8 Thanks: 0 
3+infini=10+infini=.... car (10+11+12+....=infini)

February 20th, 2019, 09:48 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
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 
February 20th, 2019, 10:06 AM  #9 
Banned Camp Joined: Feb 2019 From: France Posts: 8 Thanks: 0  
February 20th, 2019, 10:12 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
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.
Last edited by skipjack; February 20th, 2019 at 10:15 AM. 