Determine the sum of the infinite geometric series

 $\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}......$

Fill in the blank:

  In the formula for sum of geometric series S_n= a(1-rⁿ)/(1-r)

r is ___________

Calculate the sum of the infinite geometric series  

$\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\frac{1}{256}+....$

Calculate the sum of the first 6 terms of the geometric series 12 + 15 + 18 + 21 + ... .

Determine the sum of the infinite geometric series:$\frac{2}{5}+\frac{4}{25}+\frac{8}{125}+...$

Calculate the sum of the first 10 prime numbers.

What is the sum of the first 12 terms of the arithmetic series: 5 - 2 - 1 + 2 + ....

What is the sum of the series: 7 + 14 + 28 + 56 + ... + 448?

What is the sum of the first 20 terms of the arithmetic series 2 + 4 + 6 + 8 + ...?

Calculate the sum of the series 2 + 5 + 8 + 11 + 14.