I think the number is 81 but I am not sure hoped that helped sorry that I am not completely positive ):
Answer:
Mary has 12 friends, and a total of 13 people including her. Or, she has 25 friends, and a total of 26 people including her.
Step-by-step explanation:
First, we know that 26 is divisible by 1, 2, 13, and 26 because (2x13) and (1x26) both equal 26 but we know that Mary has more than 1 friend and if Mary is also added to the group where the candy is divided, that means that 1 and 2 are both out because Mary has more than 1 friend so 1 cannot be the answer and if Mary has 2 friends, that means that the candy would have to be divided 3 ways which is not possible evenly so the answer is either 12 friends or 25 friends.
I just plugged all three of these equations into a calculator and A and C both equal 0.
Hope this helped.
Answer:
a) -8/9
b) The series is a convergent series
c) 1/17
Step-by-step explanation:
The series a+ar+ar²+ar³⋯ =∑ar^(n−1) is called a geometric series, and r is called the common ratio.
If −1<r<1, the geometric series is convergent and its sum is expressed as ∑ar^(n−1) = a/1-r
a is the first tern of the series.
a) Rewriting the series ∑(-8)^(n−1)/9^n given in the form ∑ar^(n−1) we have;
∑(-8)^(n−1)/9^n
= ∑(-8)^(n−1)/9•(9)^n-1
= ∑1/9 • (-8/9)^(n−1)
From the series gotten, it can be seen in comparison that a = 1/9 and r = -8/9
The common ratio r = -8/9
b) Remember that for the series to be convergent, -1<r<1 i.e r must be less than 1 and since our common ratio which is -8/9 is less than 1, this implies that the series is convergent.
c) Since the sun of the series tends to infinity, we will use the formula for finding the sum to infinity of a geometric series.
S∞ = a/1-r
Given a = 1/9 and r = -8/9
S∞ = (1/9)/1-(-8/9)
S∞ = (1/9)/1+8/9
S∞ = (1/9)/17/9
S∞ = 1/9×9/17
S∞ = 1/17
The sum of the geometric series is 1/17
