Mathematics (science, engineering, agriculture and medicine)
1. Multiple-choice question: This topic is entitled ***8 small questions, with 5 points for each small question and 40 points for * * *. Only one of the four options given in each small question meets the requirements of the topic.
1. If a < 0, > 1, then (d)
A.a> 1，b>0 B.a> 1，b 0。
5.u.c.o.m
Then this sequence is called B sequence.
(1) The first item is 1. Is the geometric series of the common ratio a class B number? Please explain the reasons;
Please make a proposition with a judgment condition in one group and a judgment in another group as the conclusion.
Judge the truth value of a given proposition and prove your conclusion;
(2) Let it be the sum of the first items of the sequence, and give the following two groups of conclusions;
Group A: ① Series B; ② This series is not a B series.
Group B: ③ Series B; ④ The series is not a B series.
Please make a proposition with one conclusion in one group as the condition and one conclusion in the other group as the conclusion.
Judge the truth value of a given proposition and prove your conclusion;
(3) If all series are series, prove that series are also series.
Solution (1) Let the geometric series satisfying the problem be, then, then
So |-|+|-|+...+|-| =
Because it is W W W K S 5. U C O M.
So the first term is 1, and the geometric series of the common ratio is a B- series.
(2) Proposition 1: If the series is B series, the series is B series.
The secondary proposition is a false proposition.
In fact, let's say that the easy-to-know sequence is a B sequence, but
From the arbitrariness of, the sequence is a b sequence, and this proposition is.
Proposition 2: If the series is B series, then the series is B series.
This proposition is true.
In fact, because the series is B series, there is a positive number m, which is true for any number.
5.u.c.o.m
Namely. therefore
So the series is B series.
(III) If the series {0} is a series, there are positive numbers, and any one has a positive number.
take notice of
Similarly: ww w w k s 5. u c o m
Remember, there is.
therefore
+
Therefore, the sequence is w.w.w.k.s.5.u.c.o.m