Sequences and Series

Arithmetic Series

Sn = n(a1 + an)/2

  • High school
  • about 3 min
  • 2 of 10 in the family
Not started
123456Each pair = 7, 3 pairs
n = 6
1+2+⋯+6=211+2+\cdots+6 = 21
Sn=n(a1+an)2=6⋅72=21S_n = \frac{n(a_1+a_n)}{2} = \frac{6\cdot7}{2} = 21

Gauss's trick: pair the first with last (1+n), second with second-to-last (2+(n-1)),... Every pair sums to n+1. Number of pairs = n/2.