Given f ( n ) = 2 n + 1 + 2 n 2 + n , Evaluate 1 f ( 1 ) + 1 f ( 2 ) + 1 f ( 3 ) + ⋯ + 1 f ( 99 )

Question

Given   f  (  n  )  =      2    n    +    1    +    2                  n        2            +      n      , Evaluate       1          f      (      1      )        +      1          f      (      2      )        +      1          f      (      3      )        +  ⋯  +      1          f      (      99      )

Holly Schmidt · Accepted Answer

The hint.Use      1                  n        +        1            +              n              =      n    +    1    −      n  and the telescopic sum.Finally, we obtain      100    −  1  =  9.

lemondedeninaug · Accepted Answer

Very simple Hint: Rationalize the denominator      1          f      (      x      )        =      1                  n            +              n        +        1              =                    n            −              n        +        1                    (              n            +              n        +        1            )      (              n            −              n        +        1            )        =      n    +    1    −      n

Given f(n)=sqrt(2n+1+2 sqrt(n^2+n)), Evaluate 1/(f(1))+1/(f(2))+1/(f(3))+...+1/(f(99))

Answered question

Answer & Explanation

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