Integral!

Probability Level 3

The number of integral terms in the binomial expansion of

( 5 1 / 2 + 7 1 / 8 ) 1024 \large \left(5^{1/2} + 7^{1/8} \right)^{1024}

is?

133 131 130 128 129 127

Parth Lohomi by Parth Lohomi , 20, India

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1 solution

Tanishq Varshney
Mar 13, 2015

GENERAL TERM IS 1024 C r 5 1024 − r 2 7 r 8 ^{1024}C_{r} 5^{\frac{1024-r}{2}} 7^{\frac{r}{8}}

just find multiple of 8 as they make the terms integer.

the first term is r = 0 r=0 and last term is r = 1024 r=1024 with common difference of 8 8

1024 = 0 + ( n − 1 ) 8 1024=0+(n-1)8

then number of terms = 129 129

2 Helpful 1 Interesting 0 Brilliant 0 Confused

too easy !

Karan Shekhawat - 6 years, 3 months ago

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