Question

Using Gauss approach
a) 1+2+3+4+...+98 I think the answer is 4851
b)1+3+5+7+...+1003 I got two answers for 503506
I wanted to make sure I did this correctly
I did 98*99/2 for the first one and 1003*1004/2 for the second on is right?

Answer 1

Welcome to Openstudy :)

Answer 2

Hi

Answer 3

I am not sure if I did that correctly and the first answer I got for b was 1006009 but the second following a previous question I got 503506 for b. Is my second answer correct and if not can you show me how to get the correct answer?

Answer 4

First is correct .For second see below
a=1,d=3-1=2,l=1003
i=a+(n-1) d
1003=1+(n-1)*2
\[n-1=\frac{ 1002 }{ 2 }=501,n=501+1=502\]
formula is
\[\frac{ n }{ 2 }\left( a+l \right)\]
where a is first term and l is last term,n=number of terms.

Answer 5

I think I got it I went back over and my answer was 252004 because 502th stage is 1003

Answer 6

\[1+2+3+4+...+98=\frac{98\times 99}{2}\] for the first one

Answer 7

4851 for the first one

Answer 8

second one is \(n^2\) were \(n\) is the number of odd numbers you have
you can find \(n\) by solving \[2n-1=1003\]

Answer 9

252004 for b