Q.
The greatest coefficient in the expansion of (1+x)40 is
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a
1.3.5....3920!220
b
1.3.5....3920!
c
40!20!
d
40!
answer is A.
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Detailed Solution
The greatest coefficient of (1+x)n is Cn2 n , if n is even=C402 40=C20 40=40!20!20!=(40.39.38….4.3.2.1)20!20!=(40.38.36….4.2)(39.37….3.1)20!20!=220(20.19.18….2.1)(1.3….39)20!20!=1.3….3920!220
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