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in Binomial Theorem, Sequences and Series by (49.1k points)
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The remainder when 3815 is divided by 13 is …

(a) 12 

(b) 1 

(c) 11 

(d) 5

1 Answer

+1 vote
by (46.9k points)
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Best answer

(a) 12

3815 = (39 – 1)15 = 3915 – 15C1 3914 (1) + 15C2 (39)13 (1)2 – 15C3 (39)12 (1)3 ... + 15C14 (39)1 (1) – 15C15 (1) 

Except - 1 all other terms are divisible by 13. 

∴ When 1 is added to it the number is divisible by 13. So the remainder is 13 – 1 = 12.

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