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The sum of the series 1 1.2 - 1 2.3 + 1 3.4 . . up to is equal to

Options

  1. A_e ( 4 e )
  2. B2 _e 2
  3. C_ e 2-1
  4. D_ e 2

Correct answer

A. _e ( 4 e )

Step-by-step solution

1 1.2 - 1 2.3 + 1 3.4 Let T_n= 1 n(n+1) = ( 1 n - 1 n+1 ) S = T ₁- T ₂+ T ₃- T ₄+ T ₅ = ( 1 1 - 1 2 )- ( 1 2 - 1 3 )+ ( 1 3 - 1 4 )- ( 1 4 - 1 5 ) . =1-2 [ 1 2 - 1 3 + 1 4 - 1 5 ]=1-2[- (1+1)+1]=2 2-1= ( 4 e )

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