SOLUTION: So I understand how summation and series sequences work but I came across a homework problem that stumped me. I can generally write a sum in summation notation really quickly but I

Algebra ->  Sequences-and-series -> SOLUTION: So I understand how summation and series sequences work but I came across a homework problem that stumped me. I can generally write a sum in summation notation really quickly but I      Log On


   

Question 812881: So I understand how summation and series sequences work but I came across a homework problem that stumped me. I can generally write a sum in summation notation really quickly but I need help with the following.
Write each sum in summation notation: 1-2+3-4+...+(-50)
I get that x=1 goes under the sigma notation and 50 goes above it but I am not able to figure out what the formula is. If you could help me I would greatly appreciate it. Thank You
Found 2 solutions by htmentor, ewatrrr:
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
This series consists of consecutive integers, but the sign alternates.
-1 raised to an even power is +1 and -1 raised to an odd power is -1. So the following summation notation will reproduce the given series:
sum%28+%28-1%29%5E%28n%2B1%29+%2A+n%2C+n=1%2C+50%29
Check:
The 1st term is %28-1%29%5E2%2A1+=+1
The 2nd term is %28-1%29%5E3%2A2+=+-2
and so on...

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

Write each sum in summation notation: 1-2+3-4+...+(-50)

When dealing with alternating + and - numbers, %28-1%29%5E%28x-1%29 often used

sum%28+x%28-1%29%5E%28x-1%29%2C+x=1%2C+50+%29