The largest coefficient in the expansion of (1+x)^(24) is


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Question Number 63832 by gunawan last updated on 10/Jul/19

$The largest coefficient in the expansion$ $of {(1 + x)}^{24} is$
Commented by kaivan.ahmadi last updated on 10/Jul/19

$y o u a r e r i g h t$ $13 t h t e r m i s m a x$ $s i n c e 24 i s e v e n \frac{24}{2} + 1 = 13 t e r m h a s m a x c o f f$
Commented by Tony Lin last updated on 10/Jul/19

$C_{12}^{24} = \frac{24!}{12! 12!} = 2704156$
Commented by kaivan.ahmadi last updated on 10/Jul/19

$12 t h t e r m h a s t h e l a r g e s t c o e f f i c i e n t$ $(\begin{matrix} 24 \\ 11 \end{matrix})$
Commented by Tony Lin last updated on 10/Jul/19

$C_{11}^{24} = 2496144 < C_{12}^{24} = 2704156$
Commented by mr W last updated on 10/Jul/19

$m a x . o f C_{r}^{n} i s w h e n r i s a s c l o s e t o \frac{n}{2}$ $a s p o s s i b l e .$ $i f n = 24 \Rightarrow r = \frac{24}{2} = 12$ $i f n = 25 \Rightarrow r = 12 o r 13$
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