infinite series sum

hello guys I want to just ask a mathematical problem here. how can i find the sum of this infinity series.

where 0<a<1

thnxs in advance.

For Infinite Summation with common ratio |r| < 1 has S = a0/(r-1) Where a0 is First term and r is common ratio.

no one here is able to solve plz chk. it will be very helpful to me.

The sum will diverge. There is no bound.

a^{1/2^{i+1}} > a^{1/2^{i}} When 0 < a < 1 so each term is greater than the previous one


shouldn’t it be a0/(1-r)?

@hideintree chk again it’s not gp here.

I think ans is inf,as (a)^(1/2^n) tends to 1 as n tends to infinity

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if we take value of a>0 then,

Even if a > 1

\lim_{x \to \infty} a^{1/2^x} = 1

So there will be no bound