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serious [3.7K]
3 years ago
5

A student government has five positions to fill and there are nine candidates running for any one of the position. how many diff

erent possibilities are there for the five positions
Mathematics
2 answers:
mixer [17]3 years ago
8 0
Each candidate has a 1/5 chance to be a student governed
4vir4ik [10]3 years ago
5 0
I think 1/5 is the answer. 
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1. Find a formula for the general term of the sequence, assuming the pattern continues and that the first term corresponds to ,
Keith_Richards [23]

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  1. an = (-1)^(n-1)·(n+2)!/3^n

  2. the sequence diverges

Step-by-step explanation:

Perhaps you're concerned with the sequence ...

  {2, -24/9, 120/27, -720/81, ...}

1. This is neither arithmetic nor geometric. Ratios of terms are -4/3, -5/3, -6/3.

The alternating signs mean one factor of the general term is (-1)^(n-1). The divisors of 3 in the term ratios indicate 3^-n is another factor. The increasing multipliers suggest that a factorial is involved.

If we rewrite the sequence factoring out (-1)^(n-1)/3^n, we have ...

  {6, 24, 120, 720, ...}

corresponding to 3!, 4!, 5!, 6!. This lets us conclude the remaining factor is (n+1)!.

The general term is ...

  \boxed{a_n=\dfrac{(-1)^{n-1}(n+2)!}{3^n}}

__

2. The magnitude of the factorial quickly outstrips the magnitude of the exponential denominator, so the terms keep getting larger and larger.

The sequence diverges.

__

3. No series are provided.

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