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The number of integral terms in the expansion of (5 12 + 7 18 )1016 is:
(2) 128
Tr+1 = 1016Cr (5 12 )1016 - r (7 18 )r = 1016Cr 5 1016 - r2 7 r8
The term is an integer when r8 and 1016 - r2 are both whole numbers.
r a multiple of 8 r is even 1016 - r is even (1016 is even)
r = 0, 8, 16, , 1016
Number of values = 10168 + 1 = 127 + 1 = 128
Answer: (2)
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