SOLUTION: 1+2+3...+81= solve it

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Question 1093154: 1+2+3...+81= solve it
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
1 + 2 + 3 + . . . + n = the sum of the first n natural numbers = 

                      = the sum of the first n terms of an Arithmetic progression
                        with the first term 1 and the common difference 1 =

                      = %28n%2A%28n%2B1%29%29%2F2.


In your case n = 81 and the sum is  %2881%2A82%29%2F2 = 81*41 = 3321.


Answer. 3321.

Solved.

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For introductory lessons on Arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1+2+3...+81= solve it
1+2+3...+80 --> 80 numbers
Make 40 pairs:
1 + 80 = 81
2 + 79 = 81
etc
40*81 = 3240
---
Add 81
--> 3321
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If you prefer remembering rules and formulas:
Sum = n*(n+1)/2 = 81*41
= 3321