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Q.

The coefficient of x20 in the expansion of 1+11!x+12!x2+…+120!x203is

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a

0

b

320!

c

32020!

d

60C20

answer is C.

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Detailed Solution

Note that, coefficient of x20 in 1+11!x+12!x2+…+120!x203coefficient of x20  in 1+11!x+12!x2+…+120!x20+121!x21+…3coefficient of x20 in  e3x=32020!
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The coefficient of x20 in the expansion of 1+11!x+12!x2+…+120!x203is