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 lengths a, a in N, a gt 1 . Let L_(1),L_(2),L_(3) ... Be points 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_(1)M_(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

ABC is a right angled triangle in which angleB=90^@ and BC=a. If n points L_1,L_2,....L_n on AB are such that AB is divided in n+1 equal parts and L_1M_1,L_2M_2,...L_nM_n are line segments parallel to BC and M_1,M_2,...M-n are on AC. Then the sum og the lengths of L_1M_1,L_2M_2,.....L_nM_n is

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

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

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

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

ABC is a right angled Delta in which angleB=90^@ and BC =a. If n points L_1,L_2,L_3,...,L_n on AB are such that AB is divided into (n+1) equal parts and L_1M_1,L_2M_2,...,L_nM_n are line segments parallel to BC and points M_1,M_2,...,M_n are on AC, then the sum of the lengths of L_1M_1,L_2M_2,...,L_nM_n is:

ABC is a right angled triangle in which /_B=90^(@) and BC=a. If n points L_(1),L_(2),"…….",L_(n) on AB are such that AB is divided in n+1 equal parts and L_(1)M_(1),L_(2)M_(2),"......,"L_(n)M_(n) are line segments parallel to BC and M_(1),M_(2),M_(3),"......,"M_(n) are on AC, the sum of the lenghts of L_(1)M_(1),L_(2)M_(2),"......,"L_(n)M_(n) is

ABC is a right angled triangle in which /_B=90^(@) and BC=a. If n points L_(1),L_(2),"…….",L_(n) on AB are such that AB is divided in n+1 equal parts and L_(1)M_(1),L_(2)M_(2),"......,"L_(n)M_(n) are line segments parallel to BC and M_(1),M_(2),M_(3),"......,"M_(n) are on AC, the sum of the lenghts of L_(1)M_(1),L_(2)M_(2),"......,"L_(n)M_(n) is