Concordia University · MATH 202

Concordia MATH 202 tutoring

Get one-to-one online help with the algebra topics assigned in your Concordia MATH 202 section. You can start with a question alone. Your tutor can help you set up a counting problem, build an induction proof or work through a complex-number calculation.

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Online 60 min: $55 CAD · Pricing Midterm & final exam help Try a free practice question Free lesson: finite sums and induction

Listed course

Course overview

Concordia MATH 202, College Algebra, develops algebraic reasoning after Elementary Functions. Its catalogue lists possible topics in progressions, counting, mathematical induction, inequalities, polynomials and complex numbers. Use your section’s outline to select the topics you need.

Check your section’s current outline and schedule with Concordia.

MATH 202 topics to review

Progressions and finite sumsPermutations and combinationsMathematical inductionInequalitiesPolynomialsComplex numbers in Cartesian and polar form

Common difficulties

Choosing permutations or combinations by whether order matters
Using the induction hypothesis without assuming the next case

Preparing for this course

Review substitution, factoring, exponent rules and the difference between an expression and a statement to prove. For progressions, distinguish a single term from the sum of several terms. The short check below tests the step from one partial sum to the next.

Registration requirements

MATH 201 or equivalent is the listed prerequisite. Program and prior-credit restrictions also apply; consult Concordia before making a registration decision.

Check the official course catalogue

Try a course problem

For each positive integer $n$ , let $S_n=\sum_{j=1}^{n}(4j+1)$ , the sum of the first $n$ terms $5,9,13,\ldots$ . Prove by induction that $S_n=n(2n+3)$ . In the induction step, name the term added to $S_k$ before using the proposed formula.

Show the reasoning

Check the starting case
When $n=1$ , the sum is $S_1=5$ , and the proposed formula gives $1(2+3)=5$ . The statement is true at its first allowed index.
Use one case to establish the next
Let $k\ge1$ be an arbitrary integer. Assume $S_k=k(2k+3)$ for this step. The next term has index $k+1$ , so it is $4(k+1)+1=4k+5$ . We must establish the next case rather than assume it.
From the definition of the sum, $\begin{aligned}S_{k+1}&=S_k+(4k+5)\\&=k(2k+3)+4k+5\\&=2k^2+7k+5\\&=(k+1)(2k+5).\end{aligned}$ Since $2k+5=2(k+1)+3$ , this is exactly the proposed formula with $n=k+1$ .
Conclude for every allowed index
The base case and the implication from an arbitrary $k$ to $k+1$ prove the identity for all integers $n\ge1$ . Adding $4k+1$ would repeat the old last term. Checking only a few numerical sums would not prove the identity for every $n$ .

Complex numbers: Cartesian and polar forms

Complex numbers are a possible topic in MATH 202. Check your current section outline before choosing this lesson.

Practise the modulus and argument, and check your quadrant. Use the powers-and-roots section if it appears in your current outline.

How tutoring can help

You can start with a counting question, an induction statement or a complex-number problem, even if you have not begun a solution. Your tutor can help you decide what is being counted, explain the steps of an induction proof or connect Cartesian and polar forms of a complex number. You can then try a different example with guidance and explain the conditions that justify each step.

Exam preparation for MATH 202

Mix questions from the topics assigned in your section. For a progression, label the term and the partial sum separately. For counting, state whether order matters and whether repetition is allowed. For induction, write the starting index, hypothesis and target before calculating. Check complex-number calculations in the representation suited to the question.

Use your section’s outline to choose the chapters to review. We work through permitted practice and comparable problems, without completing graded assignments or exams on your behalf.

Independent practice

Free practice and study guides for MATH 202

16 min

Finite Sums and Induction: Prove the Next Case

Distinguish a term from a partial sum, prove a geometric-sum identity and spot a circular argument. Three original exercises move from guided calculation to a proof with a shifted starting index.

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MATH 202 · official course reference