We know that -1 = i

so, the question can be written as i-i-i-i.........till infinity, [if I have understood the question properly.]

The first two i cancel out. So the expression becomes -i-i-i-....till infinity.

Take the negative sign common.

you get -{i+i+i........till infinity}

the thing within the bracket is an infinite A.P. with common difference > 0 and the sum of such a series is always = infinity.

So the final answer is  {-infinity}, if my interpretetion of your question is correct.

      

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