17 By giving
x
appropriate numerical values in the expansion of
(1+x)^(2n)
, where
n
is a positive integer, prove that (a)
^(2n)C_(1)+^(2n)C_(2)+^(2n)C_(3)+cdots+^(2n)C_(2n-1)=2(2^(2n-1)-1)
(b)
1-2^(2n)C_(1)+4^(2n)C_(2)-8^(2n)C_(3)+cdots+(-2)^(2n)=1
(c)
^(2n)C_(0)+^(2n)C_(2)+^(2n)C_(4)+cdots+^(2n)C_(2n)=^(2n)C_(1)+^(2n)C_(3)+^(2n)C_(5)+cdots+^(2n)C_(2n-1)=2^(2n-1)