This question is from Ponnusamy and Silvermann's Complex variables with applications ( Chapter : Entire and meromorphic functions).
Construct an analytic function f in |z|<R such that f has zeroes only at z=-R +1/n $n \in \mathbb{N}$.
I can 't use weierstrass's product theorem as sequence has a finite ;limit point . Also , $\sum_{n=1}^{\infty} 1/{a_n}^p $ will diverge for all p , where $a_n$= -R+1/n so , f(z) = $\prod_{n=1}^{\infty} (1-z/a_n) \times exp(z+ z^2 /2 +z^3/3 + z^p/p)$ can't be the required function.
I don't have any other ideas on how to find the series.
Kindly help me.