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Jumat, 19 Oktober 2012

Barisan dan Deret #1


$latex \bf{Barisan\ dan\ Deret\ Aritmatika}$
$latex \bf{Barisan\ dan\ Deret\ Geometri}$
$latex Contoh\ barisan$
$latex 2,\ 5,\ 8,\ 11,\ ...$
$latex Contoh\ barisan$
$latex 2,\ 6,\ 18,\ 54,\ ...$
$latex Contoh\ deret$
$latex 2+5+8+11+...$
$latex Contoh\ deret$
$latex 2+6+18+54+...$
$latex Bentuk\ baku$
$latex a,\ a+b,\ a+2b,\ a+3b,\ ...$
$latex Bentuk\ baku$
$latex a,\ ar,\ ar^2,\ ar^3,\ ...$
$latex Bentuk\ lain$
$latex a-b,\ a,\ a+b,\ a+2b,\ ...$
$latex Bentuk\ lain$
$latex \frac{a}{r},\ a,\ ar,\ ar^2,\ ...$
$latex Suku\ke-n$
$latex U_{n}=a+(n-1)b$
$latex Suku\ke-n$
$latex U_{n}=a.r^{n-1}$
$latex "Beda"$
$latex b=U_{n}-U_{n-1}$
$latex "Rasio"$
$latex r=\frac{U_{n}}{U_{n-1}}$
$latex Suku\ tengah$
$latex 2U_{t}=U_{1}+U_{n}$
$latex Suku\ tengah$
$latex {U_{t}}^2=U_{1}.U_{n}$
$latex Jumlah\ n\ suku$
$latex S_{n}=\frac{n(U_{1}+U_{n})}{2}$
$latex Jumlah\ n\ suku$
$latex S_{n}=\frac{a(r^n-1)}{r-1},\quad r>1$
$latex S_{n}=\frac{n\big(2a+(n-1)b\big)}{2}$
$latex S_{n}=\frac{a(1-r^n)}{1-r},\quad r<1$
$latex Sisipan\ k\ suku$
$latex b\acute {}=\frac{b}{k+1}$
$latex Sisipan\ k\ suku$
$latex r\acute {}=\sqrt[k+1]{r}$
$latex Rumus\ khusus$
$latex U_{m}-U_{n}=(m-n)b,\quad m>n$
$latex Rumus\ khusus$
$latex r^{m-n}=\frac{U_{m}}{U_{n}},\quad m>n$
$latex U_{n}=S_{n}-S_{n-1}$
$latex U_{n}=S_{n}-S_{n-1}$
 $latex \frac{S_{n\acute {}}}{S_{n}}=\frac{n\acute {}}{S_{n}}$
 $latex \frac{S_{n\acute {}}}{S_{n}}=\frac{n\acute {}}{S_{n}}$


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