the radius of a cylindrical construction pipe is 2.5 ft. if the pipe is 21 ft long, what is its volume? use the value 3.14 for p
2 answers:
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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,
So : 
?
First, you want to bring everything together on the top of the fraction.
12=24/2 so you can have
Add like terms -- 12 +24 = 36
Now we are at
Which is the lowest possible simplified version while remaining at exact value.
Feel free to check my math! I kinda did this off the top of my head.
First, you want to bring everything together on the top of the fraction.
12=24/2 so you can have
Add like terms -- 12 +24 = 36
Now we are at
Feel free to check my math! I kinda did this off the top of my head.