<s>[INST] Progessive terms adding and minusing What is the value of
$$1+2+3-4+5+6+7-8+9+10+11+12...+97+98+99-100 \ ?$$
Any help is appreciated, thank you!
I added the terms as an AP then subtracted 10 then all the numbers that were missed out, not sure if this is right though.
 [/INST] If you rearrange the terms, you can write it as:
$1+2+3+5+6+7+9+10+...+98+99-4-8-...-100=1+2+3+4+...+100-2(4+8+12+...+100)= 
1+2+...+100-2\cdot 4(1+2+...+25)=\frac{100(100+1)}{2}-2\cdot4\frac{25(25+1)}{2}$.
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