please especially answer b and c section

2. Consider a one-dimensional chain of alternating positive and negative ions. (a) Show that the potential energy of an ion in this hypothetical crystal is U(r)=kre2 where =2ln2 (the Madelung constant), and r is the interionic spacing. [Hint: Make use of the series expansion for ln(1+x).] (b) What is the significance of Madelung constant? (c) When modeling systems at the nano scale, we consider electrostatic interactions as long-range (they are effective even at 10nm distances), while others like the induced dipole-induced dipole interactions are short range (they die off by 1nm ). Explain why in relation to the Madelung constant as well as other interaction potentials that you consider is relevant