array |c|c|c|c|c|c| x_i & 1 & 2 & 3 & & n f_i & 1 & 2⁻¹ & 2⁻² & & 2^ -(n-1) array What is _i^n x_i f_i equal to?

Step-by-step solution

x_i f_i=1.1+ 2 2 + 3 2^2 + + n 2^ n-1 ...(i) and 1 2 x_i f_i= 1 2 + 2 2^2 + + n-1 2^ n-1 + n 2^n ...(ii) (i) - (ii) gives aligned & (1- 1 2 ) x_i f_i= [1.1+ 2-1 2 + 3-2 2^2 + 4-3 2^3 + + 1 2^ n-1 ]- n 2^n & 1 2 x_t f_i= [1+ 1 2 + 1 2^3 + 1 2^4 + + 1 2^ n-1 ]- n 2^n aligned aligned 1 2 x_i f_t & = 1 (1- 1 2^n ) 1- 1 2 - n 2^n & = 2 (2^n-1 ) 2^n - n 2^n x_i f_i & = 2^ n+1 -n-2 2^ n-1 aligned