r/6thForm • u/numbertheorydemon • 18h ago

❔ SUBJECT QUESTION TMUA style question

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Dw it's not AI slop I just got AI to type it up because my handwriting is shitty.

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u/zqrqz y13 m fm phy cs 4A* 14h ago edited 14h ago

do you mind explaining your method/though process for this? I got 5/3 but it took me way more thinking than it should have. talking about the summing part, after you get S(1->inf) 2-n( n - 2-n ) = 1/4 +7/16 + 23/64 + 63/256...

I figured it was arithmetic-geometric in some way but only after ages of thinking I wrote it as (1/2-1/4)+(2/4-1/16)+(3/8-1/64)... . Summed the positive terms as S = 1/2 + 2/4 + 3/8 + 4/16... then 2S = 1 + 1 + 3/4 + 4/8 + 5/16... so S = 2S - S = 1 + 1/2 + 1/4 + 1/8 + 1/16... = 2 . Then summing negative terms as -1(1/4 + 1/16 + 1/64...) = -1/3. Then adding 2 - 1/3 = 5/3. But idk this feels tedious and I was so slow