1) C0 + C1 + C2 + .................. + Cn = 2n
2) C0 + C2 + C4 + .................. + Cn = 2n-1 (Obviously, n will be even)
3) C1 + C3 + C5 + .................. + Cn = 2n-1 (Obviously, n is odd)
4) C1 + 2C2 + 3C3 + .................. + nCn = n.2n-1
5) C02 + C12 + C22 + .................. + Cn2 = 2nCn
6) C1/C0 + 2 C2/C1 + 3 C3/C2 + ....................... + n Cn/Cn-1 = n(n + 1)/2
7) C0Cr +C1Cr+1 + C2Cr+2 + ....................... + Cn-rCn = (2n)! / (n - r)! (n + r)!
8) a0 , a1 , a2 , a3 ...................... , an in A.P. Then :
a0C0 + a1C1 + a2C2 + ....................... + anCn = (a0 + an)2n-1
9) C0 + (C0 + C1) + (C0 + C1 + C2) + ............ + (C0 + C1 + C2
+ .................. + Cn) = n(2n-1) - 2n
10) mC0.nCr + mC1.nCr-1 + .......................... + mCr.nC0 = m+nCr
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