Question

tommy do this instead then

Answer 1

Answer: (2) 1010025

Step-by-step explanation:

Let's find the sum of 1+3+5+7+...+2007+2009

Let's use the formulas for an arithmetic progression:

$a_1=1\ \ \ a+2=3\\d=a_2-a_1\\d=3-1\\d=2$

$a_1 =1\ \ \ \ a_n=2009\\a_n=a_1+(n-1)d\\\Rightarrow\ 2009=1+(n-1)2\\\Rightarrow \ 2009=1+2n-2\\\Rightarrow\ 2009=-1+2n\\\Rightarrow\ 2010=2n$

Divide both parts of the equation by 2:

$1005=n$

Hence,

$\displaystyle\\S=\frac{a_1+a_n}{2} n\\\\S=\frac{1+2009}{2}1005\\\\S=\frac{2010}{2} 1005\\\\S=1005*1005\\\\S=1010025$