let S= 1/2 + 3/4 + 5/8 + 7/16 ... ∝
2S = 1 + 3/2 + 5/4 + 7/8 ...∝
2S - S = S = 1 + (3/2 - 1/2) + (5/4 - 3/4) + (7/8 - 5/8) ...∝ Leaving the 1st term of 2s , we subtract (2nd term of 2S- 1st term of S) , (3rd term of 2S - 2nd term of S ) and so on
Hence S= 1 + 1+ (1/2 + 1/4 + 1/8 ...∝)
Leaving the 1st term i.e. 2 (1+1) , the remaining terms are in infinite G.P. upto ∝ with r = 1/2,
Summation of terms in inifinte GP = a/(1-r) where a is 1st term
S = 2 + ((1/2) / (1-(1/2))) = 2 + 1 = 3
