Series - Arithmetic Series - Geometric Series - Some Finite Series - Infinite Series

Minggu, 09 Agustus 2020

Arithmetic Series

 

Initial term: a₁

Nth term: a_n

Difference between successive terms: d

Number of terms in the series: n

Sum of the first n terms: S_n

 

     •        a_n = a_{n – 1} + d = a_{n – 2} + 2d = … = a_n  + (n – 1) d

     •        a₁ + a_n  = a₂ + a_{n – 1}  = … = a₁ + a_{n + 1 – i}   

Geometric Series

 

Initial term: a₁

Nth term: a_n

Common ratio: q

Number of terms in the series: n

Sum of the first n terms: S_n

Sum to infinity: S

 

     •        a_n  = qa_{n – 1} = a₁ q^{n – 1}

     •        a₁ · a_n  = a₂ · a_{n – 1} = … = a_i · a_{n + 1 – i}

 

Some Finite Series

Number of terms in the series: n

 

Infinite Series

 

Sequence: {a_n}

First term: a₁

Nth term: a_n

 

•        Infinite Series

    

•        Nth Partial Sum

   

•        Convergence of Infinite Series

   

•        Nth Term Test

   

 

 

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Labels: Mathematician

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