History of Hindu Mathematics: A Source Book v2.c17.s7.41

v2.c17.s7.41

Then dividing the foregoing equations by b₁ + 1, b₂ + 1,, respectively, and adding together, we get Σ x (1/(b₁ + 1) + 1/(b₂ + 1) + + 1/(b_n + 1)) + (k₁/(b₁ + 1) + k₂/(b₂ + 1) + + k_n/(b_n + 1)) = (n - 1)Σ x. \therefore \Sigma x = & (k_1/(b_1 + 1) + k_2/(b_2 + 1) + \dots + k_n/(b_n + 1)) / & \div (b_1/(b_1 + 1) + b_2/(b_2 + 1) + \dots + b_n/(b_n + 1) - 1). Whence x_r = & { (k_r + b_r k_1)/(b_1 + 1) + (k_r + b_r k_2)/(b_2 + 1) + \dots + (k_r + b_r k_{r-1})/(b_{r-1} + 1) / & + (k_r + b_r k_{r+1})/(b_{r+1} + 1) + \dots + (k_r + b_r k_n)/(b_n + 1) - (n - 2)k_r } / & \div (b_r + 1)(b_1/(b_1 + 1) + b_2/(b_2 + 1) + \dots + b_n/(b_n + 1) - 1).