If `A_k=[[k,k-1],[k-1,k]]`, then `|A_1|+|A_2|+.......+|A_2015|=`

Let A_1, A_2 ,....... A_n be the n points on the straight-line y = px + q. The coordinates of A_k is (x_k, y_k) , where k = 1,2,.... n such that x_1, x_2 , ......, x_n are in arithmetic progression. The coordinates of A_2 is (2, –2) and A_24 is (68, 31). The y-ordinates of A_8 is

Let C_k = .^nC_k, for 0 lt= k lt=n and A_k = ((C_(k-1)^2,0), (0,C_k^2)) for k gt= 1 and A_1+A_2+...+A_n = ((k_1,0), (0,k_2)), then

If a_k is the coefficient of x^k in the expansion of (1+x+x^2)^n for k = 0, 1, 2, ......., 2n then a_1+2a_2+3a_3+...+2na_(2n)=

If a_k is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k = 0,1,2,……….,2n then a_1 +2a_2 + 3a_3 + ………+2n.a_(2n) =

If a_k is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k = 0,1,2,……….,2n then a_1 +2a_2 + 3a_3 + ………+2n.a_(2n) =

Let a1,a2,a3 ...... a11 be real numbers satisfying a_1 =15, 27-2a_2 > 0 and a_k= 2a_(k-1) - a_(k-2) for k=3,4,.....11 If (a1^2 +a2^2.......a11^2)/11 = 90 then find the value of (a_1+a_2....+a_11)/11

Let a1,a2,a3 ...... a11 be real numbers satisfying a_1 =15, 27-2a_2 > 0 and a_k= 2a_(k-1) - a_(k-2) for k=3,4,.....11 If (a1^2 +a2^2.......a11^2)/11 = 90 then find the value of (a_1+a_2....+a_11)/11

Let a1,a2,a3 ...... a11 be real numbers satisfying a_1 =15, 27-2a_2 > 0 and a_k= 2a_(k-1) - a_(k-2) for k=3,4,.....11 If (a1^2 +a2^2.......a11^2)/11 = 90 then find the value of (a_1+a_2....+a_11)/11

If a_k=1/(k(k+1)) for k=1 ,2……..,n then prove that (sum_(k=1)^n a_k)^2 =n^2/(n+1)^2

Let a_1,a_2,a_3,.......a_11 be real number satisfying a_1=15,27-2a_2gt0 anda_k=2a_(k-1)-a_(k-2) for k=3,4,.....11. If (a_1^2+a_2^2+......a_11^2)/11=90, then the value of (a_1 +a_2+.....a_11)/11 is equal to