Using divergent questions at the start of a lesson provides the teacher with an opportunity to assess the views and understanding of the class. This is a great way to start a lesson as it immediately generates discussion and student engagement. Ultimately, divergent questions should be used whenever the teacher wants students to engage in discussion and debate.ĭue to their open-ended nature, divergent questions will allow students to express a range of views and thoughts on a specific topic allowing for agreement, disagreement and discussion.ĭivergent questions can be used at the start of a lesson to provide students with an opportunity to express their views and thoughts on the topic being taught. Teachers can use divergent questions at any point in a lesson. There is less need and opportunity for discussion to follow in this instance but it can be worth asking the student to explain their answer to check their reasons for selecting that specific response can be justified. The teacher will have an expectation of the student’s response and will be able to check understanding accordingly. The solution would be one which is most likely to resolve the problem in most cases.
Specifically, when there is a clear right or wrong answer or where a specific solution is most likely to be the optimal solution.įor example, the teacher can share a problem with the students and ask a convergent question asking them to propose a solution to the problem. Typically, convergent questions are used when the teacher wants to check a student’s understanding on of a topic. Find its value in case of convergent.Teachers can use convergent questions at any point in a lesson.Ĭommonly, convergent questions are used at the start of a lesson to assess student understanding of the topic to be taught in that lesson or to check what the students are able to remember from the previous lesson.Ĭonvergent questions are also commonly used at the end of the lesson as part of a plenary activity to check understanding.īut divergent questions can be used at any point in a lesson where the teacher feels they will be beneficial to student progress. Let converges to ‘l’ and converges to ‘m’. Let converges to s, let k be a non-zero fixed number then converges to ks.Ĥ.
Convergent and divergent sequences series#
if positive terms of convergent series change their sign, then the series will be convergent.ģ. the convergence and divergence of an infinite series is unchanged addition od deletion of a finite number of terms from it.Ģ. Oscillatory series- when Sn does not tends to a unique limit (finite or infinite), then it is called Oscillatory series. ĭivergent series– when Sn tends to infinity then the series is said to be divergent. Infinite series- If is a sequence, then is called the infinite series.Ĭovergent series – suppose n→∞, Sn→ a finite limit ‘s’, then the series Sn is said to be convergent. Here we can see that, the sequence Sn is divergent as it has infinite limit. As we can see that the sequence Sn is convergent and has limit 1.Įxample-2: consider a sequence Sn= n ² + (-1) ⁿ.
Note- a sequence which neither converges nor diverges, is called oscillatory sequence.Ī sequence is null, when it converges to zero.Įxample-1: consider a sequence 2, 3/2, 4/3, 5/4, ……. Oscillatory sequence- when a sequence neither converges nor diverges then it is an oscillatory sequence.
That means the limit of a sequence Sn will be always finite in case of convergent sequence.ĭivergent sequence- when a sequence tends to ±∞ then it is divergent sequence. Convergent sequence- A sequence Sn is convergent when it tends to a finite limit.
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