# 43 Lecture

## MTH101

### Midterm & Final Term Short Notes

## Additional Convergence tests

An alternating series is a series whose terms alternate in sign. The alternating series test states that if an alternating series satisfies the conditions that the absolute value of the terms decreases and approaches zero as the index approaches

**Important Mcq's**

Midterm & Finalterm Prepration

Past papers included

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**Which of the following tests is used to determine if a series is absolutely convergent?**

A) Ratio test

B) Integral test

C) Root test

D) Comparison test

Answer: C) Root test

**Which of the following series is convergent?**

A) ? n=1 to infinity (1/n)

B) ? n=1 to infinity (1/(n^2))

C) ? n=1 to infinity (1/n^3)

D) ? n=1 to infinity (n^2)

Answer: B) ? n=1 to infinity (1/(n^2))

**Which of the following convergence tests is based on comparing the given series with a simpler series whose convergence or divergence is known?**

A) Root test

B) Ratio test

C) Comparison test

D) Integral test

Answer: C) Comparison test

**Which of the following series is divergent?**

A) ? n=1 to infinity (1/2^n)

B) ? n=1 to infinity (1/n!)

C) ? n=1 to infinity (n/2^n)

D) ? n=1 to infinity (1/n)

Answer: B) ? n=1 to infinity (1/n!)

**Which of the following tests is used to determine if a series is conditionally convergent?**

A) Alternating series test

B) Divergence test

C) Integral test

D) Comparison test

Answer: A) Alternating series test

**Which of the following tests can be used to determine the convergence of a series with positive terms?**

A) Divergence test

B) Ratio test

C) Integral test

D) Root test

Answer: D) Root test

**Which of the following tests is used to determine the convergence of an alternating series?**

A) Ratio test

B) Integral test

C) Root test

D) Alternating series test

Answer: D) Alternating series test

**Which of the following tests can be used to determine the convergence of a series with negative terms?**

A) Integral test

B) Comparison test

C) Root test

D) Divergence test

Answer: B) Comparison test

**Which of the following series is convergent?**

A) ? n=1 to infinity (n/2^n)

B) ? n=1 to infinity (1/n^2 + 2)

C) ? n=1 to infinity (1/ln(n))

D) ? n=1 to infinity (n^(3/2)/(n^2 + 1))

Answer: A) ? n=1 to infinity (n/2^n)

**Which of the following convergence tests is used to determine the convergence of a series with non-negative terms, but whose terms do not approach zero?**

A) Ratio test

B) Root test

C) Integral test

D) Divergence test

Answer: D) Divergence test

**Subjective Short Notes**

Midterm & Finalterm Prepration

Past papers included

Download PDF
**What is the comparison test for convergence of infinite series?**

**Answer: **The comparison test for the convergence of an infinite series is a method of determining whether a given series converges or diverges by comparing it with another series.

**What is the ratio test for convergence of infinite series?**

**Answer: **The ratio test is a convergence test for infinite series. It states that if the limit of the ratio of consecutive terms of a series is less than 1, then the series converges absolutely.

**What is the root test for convergence of infinite series?**

**Answer: **The root test is a convergence test for infinite series. It states that if the limit of the nth root of the absolute value of the nth term of a series is less than 1, then the series converges absolutely.

**What is the integral test for convergence of infinite series?**

**Answer: **The integral test is a convergence test for infinite series. It states that if the integral of the function corresponding to the series converges, then the series converges.

**What is the alternating series test for convergence of infinite series?**

**Answer:** The alternating series test is a convergence test for infinite series in which the terms alternate in sign. It states that if the absolute value of the terms decrease monotonically to 0, then the series converges.

**What is the alternating series error bound?**

**Answer: **The alternating series error bound is an estimate of the error involved in approximating the sum of an alternating series with a finite number of terms.

**What is the Cauchy condensation test for convergence of infinite series?**

**Answer: **The Cauchy condensation test is a convergence test for infinite series. It states that if the terms of a series decrease monotonically to 0, then the series converges if and only if the corresponding series obtained by taking the sum of powers of 2 of the terms converges.

**What is the absolute convergence test for infinite series?**

**Answer: **The absolute convergence test is a convergence test for infinite series. It states that if the absolute value of each term of a series converges, then the series converges absolutely.

**What is the p-series test for convergence of infinite series?**

**Answer: **The p-series test is a convergence test for infinite series of the form 1/n^p, where p is a positive number. It states that if p > 1, then the series converges; if p <= 1, then the series diverges.

**What is the limit comparison test for convergence of infinite series?**

**Answer: **The limit comparison test is a method of determining whether a given series converges or diverges by comparing it with another series. It states that if the limit of the ratio of the terms of the two series is a positive constant, then the two series either both converge or both diverge.