Difference between revisions of "1960 AHSME Problems/Problem 20"
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By the [[Binomial Theorem]], each term of the expansion is <math>\binom{8}{n}(\frac{x^2}{2})^{8-n}(\frac{2}{x})^n</math>. | By the [[Binomial Theorem]], each term of the expansion is <math>\binom{8}{n}(\frac{x^2}{2})^{8-n}(\frac{2}{x})^n</math>. | ||
− | We want the exponent of x to be <math>7</math>, so | + | We want the exponent of <math>x</math> to be <math>7</math>, so |
<cmath>2(8-n)-n=7</cmath> | <cmath>2(8-n)-n=7</cmath> | ||
<cmath>16-3n=7</cmath> | <cmath>16-3n=7</cmath> |
Revision as of 01:19, 13 May 2018
Problem
The coefficient of in the expansion of is:
Solution
By the Binomial Theorem, each term of the expansion is .
We want the exponent of to be , so
If , then the corresponding term is
The answer is .
See Also
1960 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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All AHSME Problems and Solutions |