# Masharti muhimu Sura ya 12: Utaratibu, Mfululizo, na Theorems za Binomial

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

Mfano na Maelekezo
Maneno (au maneno ambayo yana ufafanuzi sawa)Ufafanuzi ni kesi nyeti(Hiari) Picha ya kuonyesha na ufafanuzi [Si kuonyeshwa katika Kamusi, tu katika pop-up kwenye kurasa](Hiari) Maneno ya Image(Hiari) Kiungo cha nje au cha ndani(Hiari) Chanzo cha Ufafanuzi
(Mfano. “Maumbile, Hereditary, DNA...”)(Mfano. “Kuhusiana na jeni au urithi”)sifa mbaya mara mbili helix https://bio.libretexts.org/CC-BY-SA; Delmar Larsen
Kamusi Entries
tofauti ya kawaidaTofauti kati ya maneno mfululizo katika mlolongo wa hesabu,$$a_n−a_{n−1}$$, ni$$d$$, tofauti ya kawaida, kwa$$n$$ zaidi ya au sawa na mbili.
uwiano wa kawaidaUwiano kati ya maneno mfululizo katika mlolongo wa kijiometri$$r$$,, ni, uwiano wa kawaida, wapi$$n$$ ni mkubwa kuliko au sawa na mbili.$$\frac{a_n}{a_{n−1}}$$
muda wa jumla wa mlolongoNeno la jumla la mlolongo ni formula$$n$$ ya kuandika muda wa mlolongo. $$n$$th mrefu ya mlolongo$$a_n$$,, ni neno katika nafasi$$n$$ th ambapo$$n$$ ni thamani katika uwanja.