Question

give an example of a divergent infinite series whose terms converge to 4

Answer 1

Take infinite series

Terms of this series is given by it corresponding sequence,

  

i. e. as we increses values of n=1,2,3,4..... terms of sequence going closer to 4. If we keep on incresing n then terms goes more closer to 4.It means that terms of sequence converges to 4.

Or more simply,

Means, terms of sequence conververges to 4.

But, Series   is divergent.

Note That : is convergent if p > 1, otherwise divergent.

​​​​​​ is divergent always, k is constant.

Thus,   is divergent as both of summation are divergent.

Hence, if is our required example.