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BITSAT2016MathematicsSequences and SeriesActual

(x+ 1 x )²+ (x²+ 1 x² )²+ (x³+ 1 x³ )² . upto n terms is

Options

  1. Ax^ 2 n -1 x²-1 x^ 2 n+2 +1 x^ 2 n +2 n
  2. Bx^ 2 n +1 x²+1 x^ 2 n+2 -1 x^ 2 n -2 n
  3. Cx^ 2 n -1 x²-1 x^ 2 n -1 x^ 2 n -2 n
  4. DNone of these

Correct answer

A. x^ 2 n -1 x²-1 x^ 2 n+2 +1 x^ 2 n +2 n

Step-by-step solution

The series is array l (x²+x⁴+x⁶+ )+ ( 1 x² + 1 x⁴ + 1 x⁶ + ) +(2+2+ . .) = x² (x^ 2 n -1 ) x²-1 + 1 x² (1- 1 x^ 2 n ) 1- 1 x² +2 n = x² (x^ 2 n -1 ) x²-1 + x^ 2 n -1 (x²-1 ) x^ 2 n +2 n = x^ 2 n -1 x²-1 x^ 2 n+2 +1 x^ 2 n +2 n array

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