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Hitunglah nilai faktorial dari .

Pertanyaan

Hitunglah nilai faktorial dari begin mathsize 14px style fraction numerator 5 over denominator 7 factorial end fraction minus fraction numerator 1 over denominator 6 factorial end fraction plus fraction numerator 24 over denominator 8 factorial end fraction end style.

Pembahasan Soal:

Dalam matematika, faktorial (!) adalah perkalian yang berurutan yang dimulai dari angka 1 sampai dengan angka yang dimaksud.

Dengan menerapkan konsep faktorial, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 5 over denominator 7 factorial end fraction minus fraction numerator 1 over denominator 6 factorial end fraction plus fraction numerator 24 over denominator 8 factorial end fraction end cell equals cell fraction numerator 5 cross times 8 over denominator 7 factorial cross times 8 end fraction minus fraction numerator 1 cross times 7 cross times 8 over denominator 6 factorial cross times 7 cross times 8 end fraction plus fraction numerator 24 over denominator 8 factorial end fraction end cell row blank equals cell fraction numerator 40 over denominator 8 factorial end fraction minus fraction numerator 56 over denominator 8 factorial end fraction plus fraction numerator 24 over denominator 8 factorial end fraction end cell row blank equals cell fraction numerator 40 minus 56 plus 24 over denominator 8 factorial end fraction end cell row blank equals cell fraction numerator 8 over denominator 8 factorial end fraction end cell row blank equals cell fraction numerator up diagonal strike 8 to the power of space 1 end exponent over denominator 7 factorial cross times up diagonal strike 8 to the power of space 1 end exponent end fraction end cell row blank equals cell fraction numerator 1 over denominator 7 factorial end fraction end cell row blank equals cell fraction numerator 1 over denominator 1 cross times 2 cross times 3 cross times 4 cross times 5 cross times 6 cross times 7 end fraction end cell row blank equals cell fraction numerator 1 over denominator 5.040 end fraction end cell end table end style 

Jadi, nilai dari begin mathsize 14px style fraction numerator 5 over denominator 7 factorial end fraction minus fraction numerator 1 over denominator 6 factorial end fraction plus fraction numerator 24 over denominator 8 factorial end fraction end style adalah begin mathsize 14px style fraction numerator 1 over denominator 5.040 end fraction end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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