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Infinite geometric series worksheets Grades 11–12

Find the sum of an infinite geometric series when −1 < r < 1.

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How to do it

When −1 < r < 1, the sum of all the terms is a₁ ÷ (1 − r).

64+48+36+...=25664 + 48 + 36 + ... = 256
r=34r = \dfrac{3}{4}|r| < 1, so the sum is finite
641−34=256\dfrac{64}{1 - \dfrac{3}{4}} = 256S = a₁ ÷ (1 − r)

Example problems

  1. 36−12+4−...=36 - 12 + 4 - ... =
  2. 16+4+1+...=16 + 4 + 1 + ... =
  3. 12−6+3−...=12 - 6 + 3 - ... =
  4. 32+8+2+...=32 + 8 + 2 + ... =

Sequences and series

  1. Arithmetic sequences
  2. Geometric sequences
  3. Writing the formula for a sequence
  4. Sigma notation
  5. Arithmetic series
  6. Geometric series
  7. Infinite geometric series
  8. Combinations (nCk)
  9. The binomial theorem