Question

Supposed p(n)=2^-n represents the nth partial sum of an infinite series Sum[s(n),n=1,Inf.]. Assume s(n) and p(n) are defined for all positive integers. What is the value of Sum[s(n),n=1,Inf.]?
A. 0
B. 1
C. 2
D. 3
E. None of the above/ cannot be determined

Answer 1

Suppose \[p(n)= \frac{1}{2^n}\] represents the nth partial sum of an infinite series:\[\sum_{n=1}^{∞}s(n)\]
Assume s(n) and p(n) are defined for all positive integers. What is the value of
\[\sum_{n=1}^{∞}s(n)?\]

Answer 2

the limit of the series is the limit of the partial sums. This limit is clearly 0 so the limit of the series is 0.