Geometric series

Question

Use the formula to evaluate the series

-3+6-12+24-...-a1

Answer 1

alternating series:

3*(-2)^N

It has to be finite, because the common ratio in absolute value is |-2}=2>1, so the infinite series diverges

The formula for geometric series is:

Sn = (r^(n+1)-1)/(r-1)

r=-2

3* (1 - (-2)^(n+1)) / "(1-(-2)) =

3 * (1 - (-2)^(n+1))/3 =

1 - (-2)^(n+1)