Evaluate 3. 31/2 . 31/4 . 31/8 . ................... upto infinity. Share with your friends Share 1 Manbar Singh answered this Let P= 3 × 31/2 × 31/4 × 31/8 × ...........upto ∞.P = 31+1/2+1/4+1/8+.......+∞ .....1Let S = 1 + 12 + 14 + 18 + ..............The above sequence is in GP with first term, a = 1 and common ratio, r = 12Now, S = a1 - r = 11-12 = 2So, P = 32 = 9 3 View Full Answer Avanish Ingle answered this Here 3 + 3 1/2 + 3 1/4 +.... 3(1+1/2+1/4+.....till infinity)Sum up to infinity of a GP is given bySn = a / (1-r) = 1 + 1/2 +1/4 ... = 1/ (1 - 1/2) = 2So,answer = 3 ^ 3 = 9 3
