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The series   converges

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CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
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  1. only for x = 0
  2. uniformly only for x ∈ [-π, π]
  3. uniformly only for x ∈  \{nπ ∶ n ∈ 
  4. uniformly for all x ∈ 

Answer (Detailed Solution Below)

Option 4 : uniformly for all x ∈ 
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Detailed Solution

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Concept:

Mn test: 

let an be series of real number then 

| Mn | 

if Mn Is convergent then an is convergent 

Calculation:

here 

|an | =  

| an |   

convergent for all x belong R .

Hence option (4) is correct

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