KUIS (susah) Tentukan suku ke-12 dari penjabaran (x+2)³⁴.... Question from @xcvi

xcvi @xcvi

July 2022 1 39 Report

KUIS (susah)
Tentukan suku ke-12
dari penjabaran (x+2)³⁴

ldrz

Jawaban:

$\rm 585.928.212.480x^{23}$

Penjelasan dengan langkah-langkah:

$\footnotesize\begin{aligned} \rm \rm U_{12}&= \rm C_{(n,r)} a^{n-r}b^r \\ \rm U_{12}&= \rm C_{(34,11)}( x^{34-11})2^{11} \\\rm U_{12}&= \rm \frac{34!}{(34 - 11)!11!} ( x^{23})2^{11} \\ \rm U_{12}&= \rm \frac{34!}{23! \times 11!} ( x^{23})2^{11} \\ \rm U_{12}&= \rm \frac{34 \times 33 \times 32 \times 31 \times 30 \times 29 \times 28 \times 27 \times 26 \times 25 \times 24 \times 23!}{23! \times 11!} ( x^{23})2^{11} \\\rm U_{12}&= \rm \frac{34 \times 33 \times 32 \times 31 \times 30 \times 29 \times 28 \times 27 \times 26 \times 25 \times 24}{ 11 \times 1 0\times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2} ( x^{23})2^{11} \\\rm U_{12}&= \rm \frac{2^{13}\times 3^{6}\times 5^{3}\times 7\times 11\times 13\times 17\times 29\times 31}{ 2^{8}\times 3^{4}\times 5^{2}\times 7\times 11} ( x^{23})2^{11} \\ \rm U_{12}&= \rm 2^{13 - 8}\times 3^{6 - 4}\times 5^{3 - 2} \times 13\times 17\times 29\times 31 ( x^{23})2^{11} \\\rm U_{12}&= \rm 2^{5 + 11}\times 3^{2}\times 5\times 13\times 17\times 29\times 31 ( x^{23}) \\\rm U_{12}&= \rm 2^{16}\times 3^{2}\times 5\times 13\times 17\times 29\times 31 ( x^{23}) \\\rm U_{12}&= \bf585.928.212.480x^{23}\\\end{aligned}$