Binomial trouble

Algebra Level 3

Find the number of integral terms in the expansion of ( 5 1 / 2 + 7 1 / 8 ) 1024 (5^{1/2} + 7^{1/8} )^{1024} .


The answer is 129.

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2 solutions

Kunal Gupta
Apr 10, 2015

Here, T r + 1 = 1024 C r 5 1024 r 2 7 r 8 T_{r+1}= ^{1024}C_{r}5^{\frac{1024-r}{2}}7^{\frac{r}{8}} Clearly, integral terms would be an intersection of the values from the set of 5 5 and 7 7 ,i.e. 1024 8 = 128 \dfrac{1024}{8} = 128 .
But, initial term is skipped, so answer= 128 + 1 = 129 128+1 =129

Manish Dash
Apr 5, 2015

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