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Get access to the detailed solutions to the previous years questions asked in IIM IPMAT exam
Finding the terms in the sequence, we see that t3 = 0, t4 = – 1/3, t5 = 0
We would notice that all the odd terms are 0, and we are also asked the sum of only even terms, so we do not need to consider those
t6 = – 1/5
We see that the even terms are in an HP: – 1, – 1/3, – 1/5, – 1/7, .......
The sum we are asked is the inverse of these terms, that is: – 1, – 3, – 5, – 7 up to 1012 terms
The sum of this AP would be 
Which is equal to – 1012 × 1012 = – 1024144