# NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 60 - 67 of 101

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## Question number: 60

Appeared in Year: 2005

### Describe in Detail

Find the sum of the series

### Explanation

## Question number: 61

» Convergence of Positive Series Test

Appeared in Year: 2009

### Describe in Detail

Test the following series for convergence.

a)

b)

Where is a convergent series of positive terms.

### Explanation

Option (a) The given series is

Here

By Cauchy’s Root test the given series is convergent.

option (a) is correct

Option (b) Using Result

… (133 more words) …

## Question number: 62

Appeared in Year: 2013

### Write in Short

Evaluate

## Question number: 63

Appeared in Year: 2014

### Describe in Detail

Find the sum of the following infinite series

### Explanation

………. eq. (A) [ Rearranging the terms]

Now we know that

Put

………. . eq. (1)

Also

… (55 more words) …

## Question number: 64

Appeared in Year: 2012

### Question

Determine if the following claim is true or false:

### Choices

Choice (4) | Response | |
---|---|---|

a. |
| |

b. |
| |

c. |
| |

d. | Question does not provide sufficient data or is vague |

## Question number: 65

Appeared in Year: 2009

### Describe in Detail

Evaluate

### Explanation

Let

Answer is zero

## Question number: 66

» Sequences and Series (Convergence)

Appeared in Year: 2016

### Describe in Detail

Let be an arbitrary positive real number define

Which of the following statements are true?

a) For all , we have

b) The sequence is monotonic

c) The sequence convergent

### Explanation

…………eq. (1)

That point (By Induction)

Result is true for

Assume that the result is true for

Result is true for

But res

… (349 more words) …

## Question number: 67

» Continuity and Differentiability

Appeared in Year: 2006

### Question

Let denote the set of all continuously differentiable real valued function defined on the real line. Define

where denotes the derivative of the function f. Pick out the true statements.

### Choices

Choice (4) | Response | |
---|---|---|

a. | A is an Infinite set. | |

b. | A is Empty set | |

c. | A is a finite and non-empty set | |

d. | All of the above |