What is the sum of an infinite geometric series if a1 = 5 and r = 1⁄3?

a. 25⁄2
b. 30
c. 15⁄2
d. 15

C

Step-by-step explanation:

The sum to infinity of a geometric series is

( - 1 < r < 1 ) ← substitute values

S( ∞ ) = = =

  Okay. :D First, I'll help you understand this concept.http://images.flatworldknowledge.com/redden/redden-fig04_x032.jpg  The credits to this image go to Flat World Knowledge. As you can see, there is one bolded line for the inequality and one dotted line. First and foremost, these lines represent the symbols of the inequalities involved. A dotted line will demonstrate a greater than or less than inequality. Meanwhile, a bolded line will show a greater than or equal to or a less than or equal to inequality. Now, let's get to the next conceptual idea. 
 You might be wondering where the lines come from. Well, the lines on the graph (of the inequalities) are basically like lines in slope-intercept form. For instance, take away the inequality symbol in an equality, like y > x. You then replace it with an equal sign, such that you get y=x. Of course, we know that this tweaked version isn't true, but this is a way to help familiarize yourself with drawing the inequality on the graph. Remember to draw the inequality like you would if the inequality were an equation. 
Now, we can get on to the shading of linear inequalities. After drawing the line and marking the graph properly, you have to shade your linear inequalities. All you should do is draw solid lines that connect to your inequalities' lines, but the tricky part is shading or drawing these lines in the right direction. If there's the inequality y< 3x-2, you have to shade downwards of that line. If you have a "greater than" or "greater than or equal to" symbol, shade above the line. If you have a "less than" or "less than or equal to" symbol, shade below the line. Anyways, the another way to remember this is to shade to the right of the line if the line is a generally more vertical than horizontal for > or > or equal to symbols. Shade to the left for < or < or equal to symbols. If the line is more horizontal, shade upwards for > or > or equal to symbols. Also, shade downwards for < or < or equal to symbols. I hope this information was easy to grasp. Please let me know if you will need help for each question on its own after learning this, and I advise that you try out this first, as I think that it will help. :D