Test the series for convergence or divergence.
∑[infinity](n=1) (-1)^n/n5^n
a. identify bn.
b. evaluate the following limit. lim n → [infinity] bn

12. decide whether each statement is always true, sometimes true, or never true. a. when corresponding points of an original figure and its reflection are connected, the resulting segments are all perpendicular to the line of reflection. b. when a point is reflected over a horizontal line, the y-coordinate of the point stays the same. answer both questions and explain

Jackie purchased 3 bottles of water and 2 cups of coffee for the family for $7.35. ryan bought 4 bottles of water and 1 cup of coffee for his family for 7.15. how much does each bottle of water cost? how much does each cup of coffee cost?

One side of a rectangle is 7 feet shorter than seven times the other side. find the length of the shorter side if we also know that the perimeter of the rectangle is 306 feet.