Consider the finite sum $\sum_{k=1}^{K}(1+X)^{m_k}$ where 0<$m_k$ <1 for all k.
Can a finite sum like this always be approximated by a function of the form $Y(X)=A(1+X)^M$ with some constant A and 0< M <1 ?
Don't know how to go about proving this.
Approximating the sum of functions of similar form?
0
$\begingroup$
summation
-
0What do you mean by "can be approximated?" For instance, the constant $0$ is an approximation, albeit a bad one. When $X$ is near $-1$, only the term with $m_k$ nearest to $0$ will dominate. When $X$ is really large, only the term with $m_k$ largest will dominate. In other ranges, other terms will be better or worse approximations – 2017-01-16
-
0Sorry you're right. This question was poorly worded. I meant only for $X>0$. And what I meant by approximated is do sums of this form converge to something like $A(1+X)^M$ for X>0. Edit: So you're basically saying no? – 2017-01-16