- #1
bruno67
- 32
- 0
Suppose I have two series
[itex]A=\sum_{n=0}^\infty a_n[/itex]
[itex]B=\sum_{n=0}^\infty b_n[/itex]
and I have estimates for the remainders of each one:
[itex]\sum_{n=N}^\infty a_n \le R^N_A[/itex]
[itex]\sum_{n=N}^\infty b_n \le R^N_B[/itex]
Consider the product series
[itex]AB=\sum_{n=0}^\infty c_n[/itex]
where [itex]c_n=\sum_{i=0}^n a_i b_{n-i}[/itex]. Is it possible to derive an estimate for the remainder of [itex]C[/itex] based on the ones for [itex]A[/itex] and [itex]B[/itex]?
[itex]A=\sum_{n=0}^\infty a_n[/itex]
[itex]B=\sum_{n=0}^\infty b_n[/itex]
and I have estimates for the remainders of each one:
[itex]\sum_{n=N}^\infty a_n \le R^N_A[/itex]
[itex]\sum_{n=N}^\infty b_n \le R^N_B[/itex]
Consider the product series
[itex]AB=\sum_{n=0}^\infty c_n[/itex]
where [itex]c_n=\sum_{i=0}^n a_i b_{n-i}[/itex]. Is it possible to derive an estimate for the remainder of [itex]C[/itex] based on the ones for [itex]A[/itex] and [itex]B[/itex]?