If the coefficient of x 6 in the expansion of 2 + x 3 3 + x 2 5 + x 3 is K , then the value of K 100 is

Question

If the coefficient of x 6 in the expansion of 2 + x 3 3 + x 2 5 + x 3 is K , then the value of K 100 is,

MARKS App · Accepted Answer

x + 2 3 x + 3 2 x + 5 3 = x 8 + x 7 2 + 2 + 2 + 3 + 3 + 5 + 5 + 5 + x 6 K + . . . . . . . Clearly, K is equal to the sum taken two at a time of 2,2 , 2,3 , 3,5 , 5,5 . ⇒ K = 2 + 2 + 2 + 3 + 3 + 5 + 5 + 5 2 - 2 2 + 2 2 + 2 2 + 3 2 + 3 2 + 5 2 + 5 2 + 5 2 2 = 2 7 2 - 4 + 4 + 4 + 9 + 9 + 25 + 25 + 25 2 = 729 - 105 2 = 624 2 = 31 2 ⇒ K 100 = 3.1 2

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