1-3+4-6+7-9+10-....-300+301
I will code it like
Number | Code |
1 | 1 |
-3 | 2 |
4 | 3 |
-6 | 4 |
Look at the numbers with odd-numbered code which I have already bolded.
The numbers of code with the form 2n+1 are with the form of 3n+1.
Look at the numbers with even-numbered code which I set the font Italic.
The numbers of code with the form 2n are with the form 3n.
1-3+4-6+7-9+10-....-300+301
= (1+4+7+10+......+301)-(3+6+9+......+300)
There are 301−14−1+1 terms in (1+4+7+10+......+301)
which is 101 terms.
There are 300−36−3+1 terms in (3+6+9+......+300)
which is 100 terms.
1-3+4-6+7-9+10-....-300+301
= (1+4+7+10+......+301)-(3+6+9+......+300)
= (1+301)(101)2−(3+300)(100)2
=303 <------ Final Answer