Answer:
see below
Step-by-step explanation:
The formula for the sum of an infinite geometric series with first term a1 and common ratio r (where |r| < 1) is ...
sum = a1/(1 -r)
Applying this to the given series, we get ...
a. sum = 5/(1 -3/4) = 5/(1/4) = 20
b. sum = d/(1 -1/t) = d/((t-1)/t) = dt/(t-1)
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The derivation of the above formula is in most texts on sequences and series. In general, you write an expression for the difference of the sum (S) and the product r·S. You find all terms of the series cancel except the first and last, and the last goes to zero in the limit, because r^∞ → 0 for |r| < 1. Hence you get ...
S -rS = a1
S = a1/(1 -r)
Answer:
Factor:
x^2+5x-300=0
(x-15)(x+20)=0
x=15 is the width
x+5=20 is the length
Step-by-step explanation:
9514 1404 393
Answer:
y = -7x
Step-by-step explanation:
The line goes through the origin, so the y-intercept is b=0.
The line goes through the point (1, -7), so has a "rise" of -7 for a "run" of 1. The slope is ...
m = rise/run = -7/1 = -7
Then the slope-intercept form equation is ...
y = mx + b
y = -7x
