Find the positive values of p for which the series converges. (Enter your answer using interval notation.)    ?

Find the positive values of p for which the series converges. (Enter your answer using interval notation.)

 

 

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  • Alvin
    Lv 4
    1 month ago

    Since your question ask from the positive value , 

    p> 1  which is 

    (1, + infinity) in interval notation is correct final answer.  

    but other statements in the your 1st answer are incorrect 

    -1 < (1/p)  < 1   

    if p is negative 

    (1/p) > (-1)   

    multiply both sides by -p  (which is positive ) 

    -1  > p  

    so the total answer without your positive restriction 

    is 

     p< -1  or p> 1   

    without your positive restriction 

    (-infinity, -1)  U  ( 1, +infinity) 

    but your answer ask for only positive answers 

    so 

    (1, + infinity) 

     

     

  • 1/p^n is the same as (1/p)^n

    For an infinite geometric sum, r^n converges when -1 < r < 1

    -1 < 1/p < 1

    -1 < 1/p

    -1/p < 1

    -1 < p

    1/p < 1

    1 < p

    p > -1 and p > 1.  The common set is p > 1.  When p > 1, then the series converges.

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