Sequences and Series

Infinite Geometric Series

S = a1/(1-q) when |q| < 1

  • High school
  • about 4 min
  • 5 of 10 in the family
Not started
S=2.000S1S2S3S4S5S6S7S8
a₁ = 1
q = 0.50
Steps: 8
S=a11−q=11−0.5=2.0000S = \frac{a_1}{1-q} = \frac{1}{1-0.5} = 2.0000

When |q|<1, we sum infinitely many terms but get a finite result. Partial sums approach S=a/(1-q). Classic example: 1+1/2+1/4+... = 2.