Question

Matt wins a "Magic the Gathering" trading card game tournament at his local game shop and is given two options as a prize:

Option A: 2 pack the first week, 8 packs the second week, 32 packs the third week, 128 packs the fourth week and so on for 6 weeks
Option B: 2500 packs of the newest set of "Magic the Gathering" cards now.

Part A: To obtain the most packs after 6 weeks, Matt should choose option A or B? ______


Part B: What is the difference in the total number of packs between the two options? _______

3. Using the geometric sequence: 2,1/2,1/8,...,1/512 , find the approximate sum
of the geometric series. ___________
(Round to the nearest whole number)

PLEASE SHOW WORK

Answer 1

next two weeks is 128 x 4 = about 500 x 4 is 2000 so it is more then 2500

2 + 8 + 32 + 128 + 512 + 2048

10 + 160 = 170 + 512 = 682 + 2048 = 2730

2730-2500=230

2+1/2+1/8+1/32+1/128+1/512+1/2048 = 2 + 1024/2048 + 256/2048 + 64/2048 + 16/2048 + 4/2048 + 1/2048 = 2 and 1365/2048 or 2.667 rounded is 3

Explanation: