Determine whether the series is convergent or divergent by expressing sn as a telescoping sum. ∞ 4 n(n + 2) n = 1

Mathematics

1 answer:

Genrish500 [490]2 years ago

4 0

Nothing more can be done to this equation as far as I know

∞ 4n(n +2)n = 1

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what is the unit rate of 3 pizzas for $19.99 and round the answer to nearest hundredth ? PLZzz HELP ASAP!!!!

kipiarov [429]

Divide 19.99 / 3

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Round to 6.66

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3 years ago

Solve m/26=-1/2 '''''''''''''''''''''''

trapecia [35]

Answer:

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Step-by-step explanation:

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2 years ago

Show that if X is a geometric random variable with parameter p, then

Lubov Fominskaja [6]

Answer:

$\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}=-\frac{p ln p}{1-p}$

Step-by-step explanation:

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

$P(X=x)=(1-p)^{x-1} p$

Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:

$X\sim Geo (1-p)$

In order to find the expected value E(1/X) we need to find this sum:

$E(X)=\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}$

Lets consider the following series:

$\sum_{k=1}^{\infty} b^{k-1}$

And let's assume that this series is a power series with b a number between (0,1). If we apply integration of this series we have this:

$\int_{0}^b \sum_{k=1}^{\infty} r^{k-1}=\sum_{k=1}^{\infty} \int_{0}^b r^{k-1} dt=\sum_{k=1}^{\infty} \frac{b^k}{k}$ (a)

On the last step we assume that $0\leq r\leq b$ and $\sum_{k=1}^{\infty} r^{k-1}=\frac{1}{1-r}$ , then the integral on the left part of equation (a) would be 1. And we have: