Question
Download Solution PDFIf f(x) = (1/x) – 1/ (x + 1), then what is the value of f(1) + f(2) + f(3) + - - - + f(10)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFf(x) = 1/x – 1/ (x + 1)
Put x = 1
⇒ f(1) = 1 – ½
Put x = 2
⇒ f(2) = ½ – 1/3
Put x = 3
⇒ f(3) = 1/3 – ¼
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Put x = 10
⇒ f(10) = 1/10 – 1/11
Adding all the functions,
⇒ f(1) + f(2) + f(3) + - - + f(10) = 1 – ½ + ½ – 1/3 + 1/3 – ¼ + - - - + 1/10 – 1/11
∴ f(1) + f(2) + f(3) + - - + f(10) = 1 – 1/11 = 10/11Last updated on Jun 11, 2025
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