SOLUTION: simplify 1-2+3-4+...+49-50+49-48+47-46+...+1.please help.thanks in advance

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Question 937614: simplify 1-2+3-4+...+49-50+49-48+47-46+...+1.please help.thanks in advance
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
1-2%2B3-4%2B%22...%22%2B49-50%2B49-48%2B47-46%2B%22...%22%2B1=highlight%280%29
There is more than one way to get to that answer.

If you are studying arithmetic sequences, you may be expected to split that sum into three sums of arithmetic sequences,
, and
sum%28+2i%2C+i=1%2C+i=25+%29=2%2B4%2B6%2B%22...%22%2B46%2B48%2B50=25%2A%282%2B50%29%2F2=650 , or
sum%28+2i%2C+i=1%2C+i=24%29=2%2B4%2B6%2B%22...%22%2B46%2B48=24%2A%282%2B48%29%2F2=600 ,
and calculate it as
, or
.
If you are not studying arithmetic sequences, it is easier to calculate it as
,
or something like that.
You can see that the first bracket is a sum of 25 terms of the form 2i-1-2i=-1 for i=1 to i=25 ,
and that the second bracket is a sum of 24 terms of the form 2i-%282i-1%29=1 for i=1 to i=24 .