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
Input m = -4 n = 2 and p = 1.5 into the expression above
7m + 2n - 8p/n
= 7(-4) + 2(2) - 8(1.5)/2
= -28 + 4 - 6
= -30
The answer is b. In b, 10 is divided from both 90 and 60, and that's gives you 9+6.
Answer:
about 7g/cm^3
Step-by-step explanation:
where p is density is equal to mass (5g) divided by volume (.689cm^3).
or
= 7.25 or approximately 7g/cm^3
or approximately .007kg/cm^3 dependent on what metric they want their answer in.
