" (c) "quad 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2))+

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n)," prove that " 1^(2)*C_(1) + 2^(2) *C_(2) + 3^(2) *C_(3) + …+ n^(2) *C_(n) = n(n+1)* 2^(n-2) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n)," prove that " + 3^(2) *C_(3) + …+ n^(2) *C_(n) 1^(2)*C_(1) + 2^(2) *C_(2) = n(n+1)* 2^(n-2) .

1^(2). C_(1) - 2^(2) . C_(2)+ 3^(2). C_(3) -4^(2)C_(4) + ...+ (-1).""^(n-2)n^(2)C_(n)=

1^(2). C_(1) - 2^(2) . C_(2)+ 3^(2). C_(3) -4^(2)C_(4) + ...+ (-1).""^(n-2)n^(2)C_(n)=

det[[ Prove that :,c^(2)a^(2),b^(2),c^(2)(a+1)^(2),(b+1)^(2),(c+1)^(2)(a-1)^(2),(b-1)^(2),[c-1)^(2)]]=4det[[a^(2),b^(2),c^(2)a,b,c1,1,1]]

Prove the equality 1^(2)+2^(2)+3^(2) . . .+n^(2)=.^(n+1)C_(2)+2(.^(n)C_(2)+.^(n-1)C_(2) . . .+.^(2)C_(2)) .

Prove the equality 1^(2)+2^(2)+3^(2) . . .+n^(2)=.^(n+1)C_(2)+2(.^(n)C_(2)+.^(n-1)C_(2) . . .+.^(2)C_(2)) .

Choose the correct answer intsqrt(1+x^2)dx is equal to(A) x/2sqrt(1+x^2)+1/2log|(x+sqrt(x+x^2))|+C (B) 2/3(1+x^2)^(3/2)+C (C) 2/3x(1+x^2)^(3/2)+C (D) (x^2)/2sqrt(1+x^2)+1/2x^2log|x+sqrt(1+x^2)|+C

C_ (0) ^ (2) + 2C_ (1) ^ (2) + 3.C_ (2) ^ (2) + ............ + (n + 1) C_ (n ) ^ (2) =