All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is
Multiply both sides by r :
Subtract the latter sum from the first, which eliminates all but the first and last terms:
Solve for :
Then as gets arbitrarily large, the term will converge to 0, leaving us with
So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18
Answer:
-14=-4m
Step-by-step explanation:
-2m-6=-6m+8
+2m.-8 +2m -8
-14=-4m
÷-4 = -4
7/2=m
m= 7/2
you need to multiply but the answer is 512
average of 4 numbers is 11 so 11*4 = 44
average of 5 numbers is 12.4 so 12.4*5 = 62
the 5th number = 62-44 = 18