`C_(0) + C_(1) + C_(2) + ……+ C_(9) = 512`

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Show that C_(0) + C_(1) + C_(2) + …. + C_(10) = 1024

C_(0) + C_(1) + C_(2) +….. C_(8) = 256

C_(1) + C_(2) + C_(3) + …… C_(6) = 63

Show that: C_(0) + C_(2) + C_(4) +…… + C_(12) = C_(1) + C_(2) + C_(3) + C_(5) + ……. + C_(11) = 2048

C_(1) + C_(2) + C_(3) + ……….. C_(7) = 127

C_(0) + C_(2) + C_(4) + C_(6) +C_(8) = C_(1) + C_(3) + C_(5) + C_(7) = 128

C_(1) + C_(2) + C_(3) + ….. C_(n) = 2^(n)-1

Prove that: C_(1) + 2C_(2) + 3C_(3) + 4C_(4) +….. + nC_(n) = n.2^(n-1)

Show that: C_0 + C_2 + C_4 + C_6 + C_8 + C_10 = C_1 + C_3 + C_5 + C_7 + C_9 = 512

Prove that : C_0 + C_1/2 + C_2/3 + ….. + C_n/(n+1) = (2^(n+1) - 1)/(n+1)