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 <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is
Multiply both sides by <em>r</em> :
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
9514 1404 393
Answer:
67.0 square units
Step-by-step explanation:
The formula for the area is ...
Area = 1/2ab·sin(C)
Area = (1/2)(14)(28)sin(20°) ≈ 67.036 . . . . square units
The area of the triangle is about 67.0 square units.
The "e" just lets you know that it's scientific notation.
Answer:
t distribution behaves like standard normal distribution as the number of freedom increases.
Step-by-step explanation:
The question is missing. I will give a general information on t distribution.
t-distribution is used instead of normal distribution when the <em>sample size is small (usually smaller than 30) </em>or <em>population standard deviation is unknown</em>.
Degrees of freedom is the number of values in a sample that are free to vary. As the number of degrees of freedom for a t-distribution increases, the distribution looks more like normal distribution and follows the same characteristics.
Answer:
P is the principal amount, $200.00.
r is the interest rate, 2% per year, or in decimal form, 2/100=0.02.
t is the time involved, 15....year(s) time periods.
So, t is 15....year time periods.
To find the simple interest, we multiply 200 × 0.02 × 15 to get that:
The interest is: $60.00
