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,(+x)^20 and (1+ x)^30`.Then `sum_(r=1)^10 A_r(B_10B_r-C_10A_r)` is equal to

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

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

If a_r is the coefficient of x^r in the expansion of (1-2x+3x^2)^n then sum_(r=0)^(2n) r a_r =

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