Identify the pattern of termsHere is an exam question of the unit infinite series and series of functions.Identify the pattern of terms and determine whether the following series is convergent 1 − 1 + 1 2 − 1 2 + 1 3 − 1 3 + 1 4 − 1 4 ⋯Am I supposed to find the n t h term?Are there any method of finding a simple general term for the series?

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Identify the pattern of termsHere is an exam question of the unit infinite series and series of functions.Identify the pattern of terms and determine whether the following series is convergent  1  −  1  +      1    2    −      1    2    +      1    3    −      1    3    +      1    4    −      1    4    ⋯Am I supposed to find the       n          t      h       term?Are there any method of finding a simple general term for the series?

Sanaa Holder · Accepted Answer

The sum of this series is   0For example for   n  ≥  3 the general term is            (      −      1              )                  n          +          1                            2              [                              n            −            1                    2                ]            For an even   n we have       S    n    =  0, while for an odd   n we have       S    n    =      1                  n        +        1            2        →  0.

Darius Nash · Accepted Answer

The sum of the first n terms of your series is      {                            0                           if           n           is even                                                  1            k                                     if           n          =          2          k          −          1           for some           k          ∈                      N                    .                        Therefore, the sum of your series, which is, by definition, the limit of the partial sums, is   0

Identify the pattern of terms Here is an exam question of the unit infinite series and series of functions. Identify the pattern of terms and determine whether the following series is convergent 1 -1+1/2 -1/2 + 1/3 - 1/3 + 1/4 - 1/4 ...

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