The number of rational terms in the binomial expansion of 4 1 4 + 5 1 6 120 is_______.

Question

The number of rational terms in the binomial expansion of 4 1 4 + 5 1 6 120 is_______.,

MARKS App · Accepted Answer

We have, 4 1 4 + 5 1 6 120 T r + 1 = C r 120 4 1 4 120 - r 5 r 6 ⇒ T r + 1 = C r 120 2 120 - r 2 5 r 6 For rational terms r = 6 λ , 0 ≤ r ≤ 120 , hence r = 0 , 6 , 12 , . . . , 120 So, total number of rational terms are 21 .

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