Answer is 2.
If u work out and put the reaulting ans in indices form,
First term = 2^1/2
Second term = 2^3/4
Third term = 2^7/8
and so on and so forth
Basically, u wish to find up till infinity.
Notice that the pattern lies in the powers of 2.
1/2, 3/4, 7/8, 15/16, 31/32 and so on and so forth.
Notice the difference between the terms and rephrase the series
accordingly.
1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... to infinity
Hence, it is a GP similar to a qn above.
a = 1/2
r = 1/2
Using formula of GP for sum to infinity when r < 1,
Sum to infinty = a/(1-r)
= 0.5(1-0.5)
= 1
What does this mean?
This means that
First term = 2^1/2
Second term = 2^3/4
Hence, following the above series to infinity,
ans will be 2^1 = 2
