Find the sum of the geometric series−3 + 4 − 16/3 + 64/9 −··· , or show that it is divergent.?

-3 + 4 - 16/3 + 64/9 - ...
= (-3)¹ (4)⁰ + (-3)¹⁻¹ (4)¹ + (-3)¹⁻² (4)² + (-3)¹⁻³ (4)³ + ...
= -3 [ (-3)¹⁻¹ (4)⁰ + (-3)¹⁻¹⁻¹ (4)¹ + (-3)¹⁻²⁻¹ (4)² + (-3)¹⁻³⁻¹ (4)³ + ... ]
= -3 [ (-3)⁻⁰ (4)⁰ + (-3)⁻¹ (4)¹ + (-3)⁻² (4)² + (-3)⁻³ (4)³ + ... ]
= -3 [ (-4/3)⁰ + (-4/3)¹ + (-4/3)² + (-4/3)³ + ... ]
= -3 ∑(n = 0,∞) (-4/3)ⁿ

∵ -4/3 < -1
∴ It is divergent