I have tried to compute the first few terms to try to find a pattern but I got
12+12+38+416+532+664
but I still don't see any obvious pattern(s). I also tried to look for a pattern in the question, but I cannot see any pattern (possibly because I'm overthinking it?) Please help me with this problem.
Answer
I=12+24+38+416+532+664+⋯
2I=1+1+34+48+516+632+⋯
2I−I=1+(1−12)+(34−24)+(48−38)+(516−416)+⋯
I=1+12+14+18+⋯=2
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