# Binomial Expansion : Finding Coefficients

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Please see the attached file for the fully formatted problems.

Find the following:

a) The coefficient of x in the expansion of

b) The coeffiecient of in the expansion of

c) The coefficient of in the expansion of

d) The coefficient of in the expansion of is equal to the coefficient of in the expansion of. Find the value of a.

e) Write down the first four terms in the expansion of in ascending powers of x.

f) Without using a calculator, evaluate to 8 significant figures.

g) If , prove that

1)

2)

3)

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##### Solution Summary

Coefficients are obtained from binomial expansions. Calculations are explained.

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Find the following:

a) The coefficient of x in the expansion of

Solution. Since , the coefficient of x in the expansion of is ZERO.

b) The coeffiecient of in the expansion of

Solution. , so only can contain term . ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

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- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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