Sketching Series

Monday, 29 October 2018

11:59 AM

Sketching convergent series (Rectangles under) 𝑓(𝑥)=﷐1﷮﷐𝑥﷮2﷯﷯ Sketching divergent series 𝑓﷐𝑥﷯=﷐1﷮𝑥𝑙𝑛﷐𝑥﷯﷯ ﷐Σ﷮𝑘=2﷮∞﷯﷐1﷮𝑘𝑙𝑛(𝑘)﷯ ⇒﷐1﷮𝑥𝑙𝑛(𝑥)﷯ ﷐2﷮𝑛﷮﷐1﷮𝑥𝑙𝑛﷐𝑥﷯﷯𝑑𝑥﷯ =﷐2﷮𝑛﷮﷐﷐1﷮𝑥﷯﷮﷐ln﷮﷐𝑥﷯﷯﷯﷯𝑑𝑥 =﷐﷐﷐ln﷮﷐﷐ln﷮﷐𝑥﷯﷯﷯﷯﷯﷮2﷮𝑢﷯ =﷐ln﷮﷐﷐ln﷮﷐𝑛﷯﷯﷯﷯−﷐ln﷮﷐﷐ln﷮﷐2﷯﷯﷯﷯ ^ ∞ as 𝑛→∞ ^ constant ﷐Σ﷮𝑘=2﷮𝑛﷯﷐1﷮﷐𝑘﷮2﷯﷯<﷐1﷮𝑛﷮1/﷐𝑥﷮2﷯﷯𝑑𝑥=﷐﷐π﷮2﷯﷮6﷯ Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings      Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings       

 

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