Question

Use the Gauss's approach to find the following sums.
A. 1+2+3+4+...+1001
B. 1+3+5+7+...+101
The sum of the sequence is?
The sum of the sequence is?

Answer 1

the gauss approach is about 6 feet under i think

Answer 2

gauss's approach (so legend has it) is to add forwards and backwards and then divide by 2

Answer 3

A. 1+2+3+4+...+1000+1001 = (1+1000)+(2+999)+(3+998)+...+(500+501)+1001

Answer 4

\[S=1+2+3+..+1000+1001\]
\[S=1001+1000+...+3+2+1\]
\[2S=1001\times 1002\]
\[S=\frac{1001\times 1002}{2}\]

Answer 5

From that we have 1001+1001+1001+...+1001+1001 exactly 501 times. So take \[1001\cdot500+1001 = 500500+1001=501501\]

Answer 6

Thanks for showing me how to work it. I can work the other problems like these one now.

Answer 7

I can show you how to do B also if you want me to.

Answer 8

Yes thats fine

Answer 9

As for B\[1+3+5+...+99+101=(1+99)+(3+97)+...+(49+51)+101\]Which is\[100+100+100+...+101\]With 25 terms equal to \(100\) This leaves us with \[25\cdot100 +101=2500+101=2601\]

Answer 10

Thanks KingGeorge

Answer 11

You're welcome.