I need help expanding this sigma notation..

[EddyBenzen122]

I was trying to expand and i got 1 + 2 + 3 + 4.. + n. But the answer key shows 1 + 2 + 3...(n -2 ) + (n-1) +n. I don't understand why there are (n -2 ) and (n-1) in the series

 

[lev888]

I was trying to expandView attachment 28600 and i got 1 + 2 + 3 + 4.. + n. But the answer key shows 1 + 2 + 3...(n -2 ) + (n-1) +n. I don't understand why there are (n -2 ) and (n-1) in the series

The 2 answers are the same. The second just includes 2 terms that come before n.

 

[HallsofIvy]

For example, if n= 8 then \(\displaystyle \sum_{k=1}^8 k= 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8\). 1+ 2+ 3+ 4+ ...+ n is 1+ 2+ 3+ 4+ ...+ 8, 1+ 2+ 3+ ...+ (n- 2)+ (n- 1)+ n is 1+ 2+ 3+ ...+ 6+ 7+ 8.

They are just different ways to represent the same sum.