1 / 2 + 1 / 6 + 1 / 12 +... 1 / N (n + 1) = 2005 / 2006, how much is n (please answer in detail, including solution ideas)

Using the sum method of elimination of split terms to do
Extract 1 / 2 to get
The original formula = 1 / 2 (1 / 1-1 / 2) + 1 / 2 (1 / 2-1 / 3) + 1 / 2 (1 / (n) - 1 / (n + 1))
1 / 2 (1-1 / (n + 1)) = 2005 / 2006 is obtained by extracting 1 / 2 and merging similar items
Then it should be OK

1 / 2 + 1 / 6 + 1 / 12 +... 1 / N (n + 1) = 2005 / 2006, how much is n (please answer in detail, including solution ideas)

1 / 2 + 1 / 6 + 1 / 12 +... 1 / N (n + 1) = 2005 / 2006, how much is n (please answer in detail, including solution ideas)

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