Hi, I wonder if I've solved the following questions correctly.

Do we always have a certain kind of formula for such kinds of question (both series estimation and errors of approximation)?

We seek an upper bound for the error of approximation of the series by the partial sum of its 7 first terms What is the right estimate? The error is co 1 0 1 1 \\. J _ f dz: = n=8 n 8 m5 4 . 84 The error is 00 1 0 1 1 k j _ f d3: = n=7 n 7 m5 4 74 The error is M8 ml\" |/\\ h 8 ml" 23' || The error is 00 1 0 1 1 o 2: sf dx=- n=8n5 7 m5 4.74 We seek an upper bound for the error of approximation of the series by the partial sum of its 5 first terms What is the right estimate? \\._/ f f / / The error is 00 2 n=5 6 1 71/2 The error is 00 0 2 n=6 1 era/2 The error is f: n=5 1 era/2 The error is if n=6 1 811/2 |/\\ IA 4/2' 5/2' 0 1 \"2:31 811/2 5 1 2 11/2 We want an upper bound estimate for the series where f (m) is a decreasing function of :c for m 2 1 . Which integral provides a correct upper bound? We want a lower bound estimate for the series Ef (n) n=3 where f (a) is a decreasing function of a for x 2 1. Which integral provides a correct lower bound? 9 E f (n) 2 3 . 11 f (x) dac On=3 9 E f (n) 2 /2 . 10 f (x) dac On=3 f (x) da On= 3 E f ( n) 2, 9 If ( n) 2/ f (x) dx n=3