What is the approximation for small x in the expression 1/(1 - x)?
1 + x + x^2.
What needs to be found based on the equality of coefficients in the expansion?
The possible values of n.
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Small x Approximations

What is the approximation for small x in the expression 1/(1 - x)?

1 + x + x^2.

p.1
Finding Coefficients in Polynomial Expansions

What needs to be found based on the equality of coefficients in the expansion?

The possible values of n.

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Small x Approximations

What is the approximation for 1000 - 0.999?

Approximately 1.001.

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Sum to Infinity of Series

What is the hint for finding the sum to infinity of the series given?

Compare coefficients with those in the expansion of (1 + ax)^n.

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Expansion of Functions in Powers

What should be done to expand (2 - 2x) in ascending powers of x?

Expand and give the range of values for x for which the expansion is valid.

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Finding Coefficients in Polynomial Expansions

What is the coefficient of x^(2n) in the expansion of (1 - 2x)^n?

(2n choose n) * 2^n.

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Coefficient Comparison in Expansions

What condition is given for the coefficients of x^2 and x^3 in the expansion of (1 + nx)^n?

The coefficients of x^2 and x^3 are equal.

Study Smarter, Not Harder
Study Smarter, Not Harder