The-number-of-integral-terms-in-the-expansion-of-5-1-2-7-1-8-1024-is-

Question Number 86496 by ram roop sharma last updated on 29/Mar/20

The number of integral terms in the

expansion of {(5^{\frac{1}{2}} + 7^{\frac{1}{8}})}^{1024} is

Commented by Serlea last updated on 29/Mar/20

1025

Commented by mr W last updated on 29/Mar/20

\underset{k = 0}{\sum^{1024}} C_{k}^{1024} 5^{\frac{k}{2}} 7^{\frac{1024 - k}{8}}

a t e r m i s i n t e g r a l w h e n

k = 8 r

\frac{1024 - 8 r}{8} = 128 - r ⩾ 0

\Rightarrow 0 ⩽ r ⩽ 128

\Rightarrow t h e r e a r e 129 i n t e g r a l t e r m s,

t h e s u m o f t h e m i s \underset{r = 0}{\sum^{128}} C_{8 r}^{1024} 5^{4 r} 7^{128 - r}

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