The-largest-coefficient-in-the-expansion-of-1-x-24-is-

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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