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)
_____
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:
5) 19/4
7) 49/5
Step-by-step explanation:
Answer:
17/12 = 1 5/12
Step-by-step explanation:
The common denominator of 4 and 3 is 12.
The equivalent fraction of 3/4 is 9/12.
The equivalent fraction of 2/3 is 8/12.
Their total is 17/12 (or 1 5/12).
Answer:
Step-by-step explanation:
