Question

Show that C₁ + C₂ + C₃ + ….. + C₇ = 127

Answer 1

Since C₀ + C₁ + C₂+ C₃ + ….. + C_n = 2ⁿ

Putting n = 7, we get

C₀ + C₁ + C₂ + ….. + C₇ = 2⁷

∴ C₀ + C₁ + C₂ +….. + C₇ = 128

But, C₀ = 1

∴ 1 + C₁ + C₂ + ….. + C₇ = 128

∴ C₁ + C₂ + ….. + C₇ = 128 – 1 = 127

Answer 2

We know that,

C 0 +C 1 +C 2 +...+C n =2^ n

Put n = 7 , we get,

C 0 +C 1 +C 2 +...+C 7 =2^ 7 =128

therefore1+C 1 +C 2 +...+C 7 =128 ...[:^ n C 0

=1]

therefore C 1 +C 2 +C 3 +...+C 7 =127