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प्रश्न
Show That C0 + C2 + C4 + C6 + C8 = C1 + C3 + C5 + C7 = 128
उत्तर
We know that,
C0 + C1 + C2 + ... + Cn–1 + Cn = 2n
Put n = 8, we get,
C0 + C1 + C2 + C3 + ... + C7 + C8 = 28 = 256 ... (1)
We know that, the sum of even coefficients is equal to the sum of odd coefficients.
∴ C0 + C2 + C4 + C6 + C8 = C1 + C3 + C5 + C7 = k ... (2)
From (1),
(C0 + C2 + C4 + C6 + C8) + (C1 + C3 + C5 + C7) = 256
∴ k + k = 256 ...[By (2)]
∴ 2k = 256
∴ k = 128
∴ C0 + C2 + C4 + C6 + C8 = C1 + C3 + C5 + C7 = 128.
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