The series converges to 1/(1-9x) for -1/9<x<1/9
Given the series is ∑ 
We have to find the values of x for which the series converges.
We know,
∑ 
converges to (a) / (1-r) if r < 1
Otherwise the series will diverge.
Here, ∑ 
is a geometric series with |r| = | 9x |
And it converges for |9x| < 1
Hence, the given series gets converge for -1/9<x<1/9
And geometric series converges to a/(1-r)
Here, a = 1 and r = 9x
Therefore, a/(1-r) = 1/(1-9x)
Hence, the given series converges to 1/1-9x for -1/9<x<1/9
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Answer:
1.43%
Step-by-step explanation:
we have that we can solve it by means of binomial, in this case m = 25. Also the probability of head is 50%. we need to know when it falls 7 times, therefore x = 7
the formula is:
P (x) = mCx * p ^ x * q ^ (m-x)
we know that p is 0.5 therefore q is equal to 0.5, replacing:
P (7) = 25C7 * 0.5 ^ 7 * 0.5 ^ (25-7)
P (7) = 25! / (7! * (25-7)!) * 0.5 ^ 7 * 0.5 ^ (25-7)
P = 0.0143
that is, the probability is 1.43%
Answer:
The odds to get a blackjack (natural) as arrangement: 128 / 2652 = . 0483 = 4.83%. 4.83% is equivalent to about 1 in 21 blackjack hands.
Answer:
B) 42:28
Step-by-step explanation:
First, let's get 12:18 simplified to make it easier to compare:
12:18 -> 4:6 - > <u>2:3</u>
Now let's check it against all the options:
A) 20:30 -> 2:3 and 2:3 = 2:3
Not our answer as it is congruent (equal too, the same as, etc)
B) We can see that the first number is larger than the second number, so without doing too much math we can see this is our answer!
42:28
(it simplifes to 6:4 -> 3:2)
(we do not have to do the following as we already have an answer, but here is the math)
C) 4:6
4:6 ->
2:3 = 2:3
D) 2:3
2:3 = 2:3
