Known sequence: 1, (1 + 1 / 2), (1 + 1 / 2 + 1 / 4), (1 + 1 / 2 + 1 / 4 + 1 / 8) (1+1/2+1/4+…… 1 / {2 Λ n – 1}). Find the sum of its first n terms

Known sequence: 1, (1 + 1 / 2), (1 + 1 / 2 + 1 / 4), (1 + 1 / 2 + 1 / 4 + 1 / 8) (1+1/2+1/4+…… 1 / {2 Λ n – 1}). Find the sum of its first n terms

1=2-11+1/2=2-1/21+1/2+1/4=2-1/41+1/2+1/4+1/8=2-1/8…… 1+1/2+1/4+…… +1 / 2 ^ (n-1) = 2-1 / 2 ^ (n-1) add the above expressions to get the sequence: 1,1 + 1 / 2,1 + 1 / 2 + 1 / 4,1 + 1 / 2 + 1 / 4 + 1 / 8 + The sum of the first n terms is 1 + (1 + 1 / 2) + (1 + 1 / 2 + 1 / 4) + (1 + 1 / 2 + 1 / 4 + 1 / 8) +