Coefficients

Task number: 3870

Determine the coefficient for the prescribed power of \(x\) in the following expressions:

  • Variant

    by \(x^{15}\) in \((x^2+x^3+x^4+\ldots)^4\)

  • Variant

    by \(x^5\) in \((1-2x)^{-2}\)

  • Variant

    by \(x^4\) in \((1+x)^{1/3}\)

  • Variant

    by \(x^k\) in \(1\over\sqrt{1-2x}\), for any \(k \ge 0\).

  • Variant

    by \(x^4\) in \((x^2-5x+6)^{-1}\).

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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