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} | + | 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 <math>x</math> to be <math>7</math>, so | We want the exponent of <math>x</math> to be <math>7</math>, so |
Revision as of 11:54, 20 December 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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
All AHSME Problems and Solutions |