Write the geometric series using summation notation.

Question

a) 1/4+1/2+1+2+...

b) -1 + −2 + −4 + −8...

Answer 1

Geometric series = ∑g₁r^n-1 for n = 1 to ∞.

If the series is alternating, add (-1)ⁿ or (-1)^n-1 depending if the series begins with a negative or a positive number.

1)

∞

∑(1/4)(2)^n-1

ⁿ⁼¹

2)

∞

∑(-1)ⁿ2^n-1

n=1