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If T_r= r r^4+4 and S_n= _ r=1 ^n t_r , then the value of 37 S₅- 7 26 is equal to

Options

  1. A13
  2. B25 26
  3. C1 2
  4. D7 26

Correct answer

A. 13

Step-by-step solution

aligned & T_r= r r^4+4 = r (r^2+2 )^2-4 r^2 = r (r^2+2 r+2 ) (r^2-2 r+2 ) & = 1 4 [ 1 r^2-2 r+2 - 1 r^2+2 r+2 ]= 1 4 [ 1 (r-1)^2+1 - 1 (r+1)^2+1 ] & S_n= 1 4 [1+ 1 2 - 1 n^2+1 - 1 (n+1)^2+1 ] & S₅= 1 4 [1+ 1 2 - 1 26 - 1 37 ]= 1 4 [ 38 37-26 1 26 37 ]= 1 4 1380 26 37 = 345 26 37 & 37 S₅- 7 26 = 338 26 =13 aligned

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