If `C_r=10C_r`, then `sum_(r=1)^10 C_(r-1)C_r` is equal to

sum_(r=1)^(n)(C(n,r))/(r+2) is equal to

For r=0,1, . . . ,10 let A_(r),B_(r) and C_(r) denote respectively, the coefficient of x^(r) in the expansions of : (1+x)^(10),(1+x)^(20) and (1+x)^(30) . Then sum_(r=1)^(10)(B_(10)B_(r)-C_(10)A_(r)) is equal to:

If sum_(r=m)^(n)hat rC_(m)=^(n+1)C_(m+1), then sum_(r=m)^(n)(n-r+1)^(r)C_(m) is equal to sum_(r=m)^(n)(n-r+1)^(r)C_(m) is equal to

The value of ""^(40) C_(31) + sum _(r = 0)^(10) ""^(40 + r) C_(10 +r) is equal to

The value of ""^(40) C_(31) + sum _(r = 0)^(10) ""^(40 + r) C_(10 +r) is equal to

The value sum_(r=1)^(10)r.(n_(C_(r)))/(n_(C_(r-1))) is equal to