4 Gina drew three small congruent circles
1 answer:
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Answer:
1) - Greater than -10 and less than 10.
2) - Greater than or equal to -10 and less than or equal to 10.
3) - Greater than or equal to -10 and less than 10.
4) Greater than -10 and less than or equal to 10.
Step-by-step explanation:
There are four form of describing that set in interval notation, which presented below:
1) - Greater than -10 and less than 10.
2) - Greater than or equal to -10 and less than or equal to 10.
3) - Greater than or equal to -10 and less than 10.
4) Greater than -10 and less than or equal to 10.
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