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MHT CET20239 May 2023Morning ShiftMathematicsInverse Trigonometric FunctionsActual

The value of ( _ n=1 ²³ ⁻¹ (1+ _ k=1 ^n 2 k ) ) is

Options

  1. A23 25
  2. B25 23
  3. C23 24
  4. D24 23

Correct answer

B. 25 23

Step-by-step solution

aligned & ( _ n=1 ²³ ⁻¹ (1+ _ k=1 ^n 2 k ) ) & = ( _ n=1 ²³ ⁻¹ (1+2 n(n+1) 2 ) ) & = ( _ n=1 ²³ ⁻¹(1+n(n+1)) ) aligned aligned & = ( _ n=1 ²³ ⁻¹ ( 1 1+ n ( n +1) ) ) & = ( _ n =1 ²³ ⁻¹ ( n +1- n 1+ n ( n +1) ) ) & = ( _ n =1 ²³ ⁻¹( n +1)- _ n -1 ²³ ⁻¹ n ) & = [ ( ⁻¹(2)+ ⁻¹(3)+ + ⁻¹(24) ) . & = ( ⁻¹(24)- ⁻¹(1) ) & = ( ⁻¹ ( 24-1 1+24(1) ) ) & = ( ⁻¹ ( 23 25 ) ) & = ( ⁻¹ ( 25 23 ) ) & = 25 23 aligned

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