Answer:
A
Step-by-step explanation:
Given the 2 equations
x = 3 - y → (1)
5x - 12 = y → (2)
Substitute x = 3 - y into (2)
5(3 - y) - 12 = y ← distribute and simplify left side
15 - 5y - 12 = y
3 - 5y = y ( add 5y to both sides )
3 = 6y ( divide both sides by 6 )
= y, that is
y = 0.5 → A
Answer:
The given series converges and
Step-by-step explanation:
Given is 108, -18, 3,...
It is an alternate series. An alternate series is convergent if:
1. The series is decreasing.
2. If the last term (n-th term) of series converges to 0.
<u>Since each next term is less than its preceding term, so it is decreasing.</u>
First term, a = 108
Second term = -18
Common ratio, r = -18/108 = -1/6
General term, aₙ = a*rⁿ = 108*(-1/6)ⁿ
<u>When n increases to infinity, the exponent term will decreases to zero, and last term (n-th term) will converge to 0 as well.</u>
Hence, the given series converges.
Now limit will be:
Hence,