Calculate in head, the sums of the following' arithmetic sequences.
i) 51+52+53+ ...+70
ii) 1 1/2+ 2 1/2 +…..12 1/2
iii)1/2+1+1 1/2+ 2 +2 1/2+…..+12 1/2

Calculate the following . Write them as products. i) (1)/(4) of (1)/(2) ii) (1)/(2) of (1)/(4) iii) (1)/(5) of (1)/(3) iv) (1)/(3) of (1)/(5) v) (1)/(6) . of (1)/(3) vi) (1)/(3) of (1)/(6)

Do the following problem. -2 1/2-1 1/2

Find the transpose of each of the following matrices: (i) [[5], [1/2], [-1]] ii) [[1, -1],[ 2, 3]] (iii) [[-1, 5, 6],[ sqrt3, -5, 6],[ 2, 3, -1]]

Calculate the following: 1) 4 x 5 (1)/(3) ii) 4 (1)/(3) x 5 iii) 1 (1)/(2) x (2)/(3) iv) (2)/(5) of 2 (1)/(2) v) 2 (1)/(2) x 5 (1)/(2) vi) 4 (1)/(3) of 4 (1)/(2)

Find the sum to n terms of the series 1^2+(1^2+2^2)+(1^2+2^2+3^2)+...

The area of the triangle whose vertices are A (1,-1,2), B (2, 1, -1) and C ( 3, -1, 2) is

Find the inverse of the following matrix using elementary operations A=[(1,2,-2),(-1,3,0),(0,-2,1)]

1/2+1/2^2+1/2^3=1/2 [__+__+__].

The centre of the ellipse 9x ^(2) + 25 y ^(2) - 18 x - 100 y - 116 = 0 is : a) (1,1) b) (-1,2) c) (-1,1) d) (1,2)