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KVPY2017MathematicsTrigonometric Ratios & Identities

The integer part of the number _ k =0 ⁴⁴ 1 k ^ ( k +1)^ is

Options

  1. A50
  2. B52
  3. C57
  4. D59

Correct answer

C. 57

Step-by-step solution

array l 1 0^ 1^ + 1 1^ 2^ + 1 2^ 3^ + 1 44^ 45^ array multiply & divided by 1^ array l 1 1^ [ 1^ 0^ 1^ + 1^ 1^ 2^ + 1^ 44^ 45^ ] 1 1^ [ (1^ -0^ ) 0^ 1^ + (2-1)^ 1^ 2^ + (45^ -44^ ) 44^ 45^ ] 1 1^ [ 1^ - 0^ + 2^ - 1^ + 45^ - 44^ ] = 1 1^ [ 45^ ] = 1 0.0174524 =57.2987 Integral part =57 array

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