Problem 1:
The Sum of the first $2008$ odd positive integer is subtracted from the sum of the first $2008$ even positive integers. Find the result.
BdMO National Higher Secondary 2008/1
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Re: BdMO National Higher Secondary 2008/1
Sum of the first $2008$ even positive integers=$2+4+6+...+n$
Sum of the first $2008$ odd positive integers=$1+3+5+7+...+n$ [Where $n$ denotes the $2008$-th term of the sequence]
Difference between the first terms of two sequence=$1$
Difference between the second terms of two sequence=$1$
So,Difference between the $n$-th terms of two sequence=$1$
So, the result=$1 \times 2008$=$2008$
Sum of the first $2008$ odd positive integers=$1+3+5+7+...+n$ [Where $n$ denotes the $2008$-th term of the sequence]
Difference between the first terms of two sequence=$1$
Difference between the second terms of two sequence=$1$
So,Difference between the $n$-th terms of two sequence=$1$
So, the result=$1 \times 2008$=$2008$
Last edited by Tasnood on Fri Feb 09, 2018 9:58 pm, edited 2 times in total.
-
- Posts:57
- Joined:Sun Dec 11, 2016 2:01 pm
Re: BdMO National Higher Secondary 2008/1
Tasnood,$0$ is not a positive integer. Now,the sum of the first $n$ even numbers is $n(n+1)$ and for the case of odd numbers,that is $n^2$.So,by the question, the answer is $2008(2008+1)-2008^2$=$2008$.