Advertisements
Advertisements
Question
Show That C0 + C2 + C4 + C6 + C8 = C1 + C3 + C5 + C7 = 128
Solution
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.
APPEARS IN
RELATED QUESTIONS
In the following expansion, find the indicated coefficient.
x3 in `(x^2 + (3sqrt(2))/x)^9`
In the following expansion, find the indicated coefficient.
x8 in `(2x^5 - 5/x^3)^8`
In the following expansion, find the indicated coefficient.
x9 in `(1/x + x^2)^18`
In the following expansion, find the indicated coefficient.
x–3 in `(x - 1/(2x))^5`
In the following expansion, find the indicated coefficient.
x–20 in `(x^3 - 1/(2x^2))^15`
Show That C0 + C1 + C2 + .... C8 = 256
Show That C0 + C1 + C2 + .... C9 = 512
Show That C1 + C2 + C3 + .... C7 = 127
Show That C1 + C2 + C3 + .... C6 = 63
Select the correct answer from the given alternatives.
The value 14C1 + 14C3 + 14C5 + ..... + 14C11 is
Select the correct answer from the given alternatives.
The value 11C2 + 11C4 + 11C6 + 11C8 is equal to
Expand (3x2 + 2y)5
Answer the following:
If the coefficient of x16 in the expansion of (x2 + ax)10 is 3360, find a
