Matematica - Multimi de numere. Probleme de numarare. Probabilitati

Multimi de numere. Probleme de numarare. Probabilitati - Intrebarea 20

Mergi la:

Fie dezvoltarea $open parentheses cube root of a squared end root plus fraction numerator 1 over denominator cube root of a squared end root end fraction close parentheses to the power of 18$ . Să se determine termenul independent de $a$ din dezvoltarea binomială.

T subscript 10

T subscript 5

T subscript 15

Raspunsul este corect.

Raspunsul este gresit.

Explicatie:

Răspuns corect: A

$T subscript k plus 1 end subscript equals C subscript 18 superscript k times open parentheses cube root of a squared end root close parentheses to the power of 18 minus k end exponent times open parentheses fraction numerator 1 over denominator cube root of a squared end root end fraction close parentheses to the power of k equals C subscript 18 superscript k times a to the power of fraction numerator 36 minus 2 k over denominator 3 end fraction end exponent times a to the power of negative fraction numerator 2 k over denominator 3 end fraction end exponent equals C subscript 18 superscript k times a to the power of fraction numerator 36 minus 4 k over denominator 3 end fraction end exponent$ .

Punem condiția: $fraction numerator 36 minus 4 k over denominator 3 end fraction equals 0 left right double arrow k equals 9$ .

Termenul căutat este $T subscript 10$ .