Final answer:
A geometric series can be expanded by multiplying the first term by the common ratio raised to different powers. The sum of an infinite geometric series can be found using the formula a / (1 - r). In this case, the expanded form of the series is 5 + 5 × 2 + 5 × 2² + 5 * 2³ + ... and the sum is -5.
Step-by-step explanation:
A geometric series is a sequence of numbers where each term is found by multiplying the previous term by a constant factor, called the common ratio. The expanded form of a geometric series can be written as:
5 + 5×2 + 5 × 22 + 5× 23 + ...
In this series, the common ratio is 2 and the first term is 5. We can rewrite it as:
5(1 + 2 + 22 + 23 + ...)
Now we can use the formula for the sum of an infinite geometric series:
Sum = a / (1 - r)
where a is the first term and r is the common ratio. Plugging in the values, we get:
Sum = 5 / (1 - 2)
Sum = 5 / (-1)
Sum = -5
The complete question is:Write the geometric series in expanded form 5σi=1 3(2)i=1is: