Question
Find the value of the summation from n equals 0 to 5 of the sum of 2 plus 2/2^n.
Type your answer in the space below and give 2 decimal places. If your answer is less than 1, place a leading "0" before the decimal point (ex: 0.48). (20 points)
Type your answer in the space below and give 2 decimal places. If your answer is less than 1, place a leading "0" before the decimal point (ex: 0.48). (20 points)
Answers
oobleck
5
∑ 2 + 2/2^n = ∑2 + ∑2/2^n
n=0
∑2 = 12
∑2 + 2/2^n = 2 + 1 + 1/2 + ... + 1/32 = 2(1 - 1/2^6)/(1 - 1/2) = 63/16
so the complete sum is 15 15/16
∑ 2 + 2/2^n = ∑2 + ∑2/2^n
n=0
∑2 = 12
∑2 + 2/2^n = 2 + 1 + 1/2 + ... + 1/32 = 2(1 - 1/2^6)/(1 - 1/2) = 63/16
so the complete sum is 15 15/16