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
Answer:
II. The sum of the residuals is always 0.
Step-by-step explanation:
A least squares regression line is a standard technique in regression analysis used to make the vertical distance obtained from the data points running to the regression line to become very minimal or as small as possible.
For any least-squares regression line, the sum of the residuals is always zero.
Basically, residuals are used to measure or determine whether or not the line of regression is a good fit or match for the data by subtracting the difference between them i.e the predicted y value and the actual y value, for the x value respectively.
Hence, the statement about residuals which is true for the least-squares regression line is that the sum of the residuals is always zero (0).
Answer:
O poles are getting flatter
Step-by-step explanation:
"Because of the force caused when Earth rotates, the North and South Poles are slightly flat. Earth's rotation, wobbly motion and other forces are making the planet change shape very slowly, but it is still round."
Hope this helps! :)
Answer:
-18root7
Step-by-step explanation:
-3root 84*3
-3root4*7*3*3
-3(2*3)root7
-18root7
Answer:
x=0
Step-by-step explanation:
2(3x - 1) + 2(4x + 5) = 8
Distribute
6x -2 +8x +10 =8
Combine like terms
14x +8 = 8
Subtract 8 from each side
14x+8-8=8-8
14x =0
Divide each side by 14
14x/14 = 0/14
x=0
