Comparison Test : Statement & Proof INFINITE SERIES #comparison #test #infinite #series

Comparision Test -1 :

  Statement : If Σu_n and Σv_n are two series of non-negative terms such that                                Back

a)                                         There is a positive integer m and k 𝞊 R⁺  , 0 ≤  u_n ≤ k v_n  ∀n ≥ m and

                      b)      Σv_n  is convergent then Σu_n is convergent.  

 Proof :

Comparison test -2 :

Statement  : If Σu_n and Σv_n are two series of non-negative terms such that 

a)                                        There is a positive integer m and k 𝞊 R⁺  ,  u_n ≥ k v_n≥ 0  ∀n ≥ m and

                         Σv_n  is divergent then Σu_n is divergent .

  Proof : 

#comparison #test #infinite #series