Evaluate 3. 31/2 . 31/4 . 31/8 . ................... upto infinity.

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

  • 4

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 by

Sn = a / (1-r) = 1 + 1/2 +1/4 ... = 1/ (1 - 1/2) = 2

So,answer = 3 ^ 3 = 9 

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