what is 100^2-99^2+98^2-97^2+96^2-95^2+....+4^2-3^2+2^2-1^2?
I need to find an expression where n is the largest number being squared. I notice that every odd number is minus and even number is a positive.

Question

what is 100^2-99^2+98^2-97^2+96^2-95^2+....+4^2-3^2+2^2-1^2? 
I need to find an expression where n is the largest number being squared. I notice that every odd number is minus and even number is a positive.

mathmath333 · Answer

$\large\tt \color{black}{100^2-99^2+98^2-97^2+96^2-95^2+....+4^2-3^2+2^2-1^2}$



if u write it in reverse it looks




$\large\tt \color{black}{2^2-1^2+4^2-3^2...........100^2-99^2}$





that is







$\large\tt \color{black}{3+7+11............+199}$

mathmath333 · Answer

$\large\tt \color{black}{sum=50\times\dfrac{199+3}{2}=5050}$

mathmath333 · Answer

where $\large\tt \color{black}{50}$ is the number of terms in the series