How do I check whether the sequence converges uniformly? f n = x n − x n + 1 = x n ( 1 − x ) , x ∈ [ 0 , 1 ]

Question

How do I check whether the sequence converges uniformly?      f    n    =      x    n    −      x          n      +      1        =      x    n    (  1  −  x  )  ,    x  ∈  [  0  ,  1  ]

Bruno Hughes · Accepted Answer

It is controlled by                                          (            1            −                                          1                                  n                  +                  1                                                      )                                n                                    (          1          −                                    n                              n                +                1                                              )                =                              (            1            −                                          1                                  n                  +                  1                                                      )                                n                                                1                          n              +              1                                      .            We know that                                          (            1            −                                          1                                  n                  +                  1                                                      )                                n                          →                  e                      −            1                          ,            so for large n,which tends to zero as   n  →  ∞

How do I check whether the sequence converges uniformly? f n </msub> = x

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