Question

Show that : C0 + C2 + C4 + C6 + C8 = C1 + C3 + C5 + C5 = 128​

Answer 1

(1 + x) ^8 = C0 + C1x + C2x^2 + C3x^3 + C4x^4 + C5x^5 + C6x^6 + C7x^7 + C8x^8

(1) putting x = 1

2^8 = C0 + C1 + C2 + C3 + C4 + C5 + C6 + C7 + C8

(2) putting x = - 1

0 = C0 - C1 + C2 - C3 + C4 - C5 + C6 - C7 + C8

Now adding equation (1) & (2) : -

2^8 = 2 ( C0 + C2 + C4 + C6 + C8)

(C0 + C2 + C4 + C6 + C8) = 2^7 = 128

Now subtracting equations (1) & (2) : -

2^8 = 2 ( C1 + C3 + C5 + C7 )

(C1 + C3 + C5 + C7 ) = 2^7 = 128

Answered by an IIT JEE ASPIRANT and all India mathematics OLYMPIAD TOPPER in class 10th