Consider applying the Limit Comparison Test on S = ∑ k = 1 ∞ ( 3 k 5 ( k − 1 ) ( k + 1 ) )a) Setup and calculate the limit in this test, comparing this series to ∑ k = 2 ∞ ( 1 k )b) Interpret the result of this limit in this test.

Question

Consider applying the Limit Comparison Test on   S  =      ∑          k      =      1              ∞        (            3      k              5      (      k      −      1      )      (      k      +      1      )        )a) Setup and calculate the limit in this test, comparing this series to       ∑          k      =      2              ∞        (      1    k    )b) Interpret the result of this limit in this test.

hayaniqWf · Accepted Answer

S  =      ∑          k      =      L              ∞                  3      k              5      (      k      −      1      )      (      k      +      1      )        =  ∑      a    k      ∑      b    R    =  ∑      1    R  a)  l      t          k      →      ∞                  a      R              b      R        =  l      t          k      →      ∞                  3              k        2                    5      (      k      −      1      )      (      k      +      1      )        =  l      t          k      →      ∞            3          5              |            1      −              1        R                    |                    |            1      +              1        R                    |              =      3    5  b) By limit compasion test, since   ∑      b    R   is divergent      ∑          k      =      2              ∞                  3      k              5      (      k      −      1      )      (      k      +      1      )       is divergent

Consider applying the Limit Comparison Test on S=sum_(k=1)^(oo) ((3k)/(5(k-1)(k+1)))

Answered question

Answer & Explanation

New Questions in Calculus 1