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Infinite Series : Geometric Progression

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Summation of series from n=2 to infinity of (pi/4)^(n/2)

I don't know if I should set the whole thing up as a power of e and then calculate it, or calculate it as geometric series.

https://brainmass.com/math/algebraic-geometry/infinite-series-geometric-progression-45851

Solution Summary

Infinite series and geometric progressions are investigated and discussed.

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Geometric series: Good learning

Use the geometric series of numbers 1, 2, 4, 8,...to find the following:

What is r, the ratio between 2 consecutive terms?
Can you please show how you get the answers in detail to help me Thanks.

Using the formula for the nth term of a geometric series, what is the 24th term?

Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?

Use the geometric series of numbers 1, 1/2, 1/4, 1/8,...to find the following:
What is r, the ratio between 2 consecutive terms?

Using the formula for the nth term of a geometric series, what is 10th term?

Using the formula for the nth term of a geometric series, what is 12th term?

What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?

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