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.
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Sign up to join this communityWhat 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.
And just to show that there's more than one way to skin a cat: Rearrange to get $$ (1+3+5+\cdots+97+99)+\Big[(2-4)+(6-8)+\cdots+(98-100)\Big] = 2500 + 25\cdot(-2) = 2450$$
If you rearrange the terms, you can write it as:
$1+2+3+5+6+7+9+10+...+98+99-4-8-...-100=1+2+3+4+...+100-2(4+8+12+...+100)=
1+2+...+100-2\cdot 4(1+2+...+25)=\frac{100(100+1)}{2}-2\cdot4\frac{25(25+1)}{2}$.
There are $25$ groups of four. The first group has "sum" $2$. The second group has sum $8$ more than the first group. The next group (assuming that $+12$ is a typo for $-12$) has sum $8$ more, and so on.
By the so-called Gauss Method, the full sum is $25$ times the average of first sum and last sum.