ABCD is a square of length a, `a in N`, a > 1. Let `L_1, L_2 , L_3...` be points on BC such that `BL_1 = L_1 L_2 = L_2 L_3 = .... 1` and `M_1,M_2 , M_3,....`be points on CD such that `CM_1 = M_1M_2= M_2 M_3=... = 1`. Then `sum_(n = 1)^(a-1) ((AL_n)^2 + (L_n M_n)^2)` is equal to :

ABCD is a square of length a,a in N ,a gt 1. Let L_1,L_2,L_3, ……. Be points on BC such that BL_1L_2=L_2L_3=….=1 and M_1,M_2M_3…. be points on CD such that CM_1=M_1M_2 =M_2M_3 =….1 Then Sigma_(n=1)^(a-1) (AL_n^2+L_nM_n^2) is equal to

A B C is a right-angled triangle in which /_B=90^0 and B C=adot If n points L_1, L_2, ,L_nonA B is divided in n+1 equal parts and L_1M_1, L_2M_2, ,L_n M_n are line segments parallel to B Ca n dM_1, M_2, ,M_n are on A C , then the sum of the lengths of L_1M_1, L_2M_2, ,L_n M_n is (a(n+1))/2 b. (a(n-1))/2 c. (a n)/2 d. none of these

What is shape of the orbital with (i) n = 2 and l = 0 , (ii) n = 2 and l = 1?

Consider three planes P_1 : x-y + z = 1 , P_2 : x + y-z=-1 and P_3 : x-3y + 3z = 2 Let L_1, L_2 and L_3 be the lines of intersection of the planes P_2 and P_3 , P_3 and P_1 and P_1 and P_2 respectively.Statement 1: At least two of the lines L_1, L_2 and L_3 are non-parallel The three planes do not have a common point

If vec aa n d vec b are two non-collinear vectors, show that points l_1 vec a+m_1 vec b ,l_2 vec a+m_2 vec b and l_3 vec a+m_3 vec b are collinear if |l_1l_2l_3m_1m_2m_3 1 1 1|=0.

If m >1,n in N show that 1^m+2^m+2^(2m)+2^(3m)+....+2^(n m-m)> n^(1-m)(2^n-1)^mdot