[" 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)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 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 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),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 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

Let a_(r) denote the coefficient of x^(r) in the expansion of ( 1 + x)^(P + q) , then

The value of sum_(r=0)^(9)(10C_(r))/(^^^10C_(r)+^(10)C_(r+1)) is equal to

sum_(r=0)^(10) (-1)^(r) (""^(10)C_(r))/(""^(r+2)C_(r)) is equal to .

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