The sum of the co-efficient of all even degree terms in x in the expansion of + , (x >1) is equal to

The sum of the co-efficient of all even degree terms in x in the expansion of + , (x >1) is equal to

1 Answer

127 votes

+

= 2[^{6}C_{0}x^{6} + ^{6}C_{2}x^{4}(x^{3} − 1) + ^{6}C_{4}x^{2}(x^{3} − 1)^{2} + ^{6}C_{6}(x^{3} − 1)^{3}]

=2[x^{6} + 15x^{7} − 15x^{4} + 15x^{8} − 30x^{5} +15x^{2} + x^{9} − 3x^{6} + 3x^{3} − 1]

Sum of coefficients of even powers of

x = 2[1 − 15 + 15 + 15 − 3 − 1] = 24

127 votes

127