TS Police SI Mains 2023 Paper 3 · Question 25

Question 25 of the TSLPRB SI Final Written Examination 2023, Paper III (Arithmetic & Reasoning) (8 April 2023). Try it first, then open the answer and explanation.

1. SI Mains 2023 Paper III · Q25 · Arithmetic · Numbers & Simplification

   Σ (x = 1 to 100) 1/(√(x − 1) + √x) =

   1. 9
   2. 10
   3. √99
   4. √100 − √9

   Σ (x = 1 to 100) 1/(√(x − 1) + √x) =

   1. 9
   2. 10
   3. √99
   4. √100 − √9
   Show answer

   Answer: (2) 10

   సమాధానం: (2) 10

   Rationalising, 1/(√(x − 1) + √x) = √x − √(x − 1), so the sum telescopes: (√1 − √0) + (√2 − √1) + ... + (√100 − √99) = √100 − √0 = 10.

   హారాన్ని అకరణీయం చేస్తే 1/(√(x − 1) + √x) = √x − √(x − 1), కాబట్టి మొత్తంలో పదాలు వరుసగా రద్దవుతాయి: (√1 − √0) + (√2 − √1) + ... + (√100 − √99) = √100 − √0 = 10.

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