Recent questions tagged number-series / GATE Overflow for GATE CSE

Find the sum to $'n'$ terms of the series $10+84+734+\dots$$\frac{9(9^n+1)}{10} +1$$\frac{9(9^n-1)}{8} +1$$\frac{9(9^n-1)}{8} +n$$\frac{9(9^n-1)}{8} +n^2$

Akash Kanase

4.1k views

Akash Kanase asked Feb 16, 2016

5 votes

2 answers

34

TIFR CSE 2015 | Part A | Question: 3
Let $|z| < 1$. Define $M_{n}(z)= \sum_{i=1}^{10} z^{10^{n}(i - 1)}?$ what is $\prod\limits_{i=0}^{\infty} M_{i}(z)= M_{0}(z)\times M_{1}(z) \times M_{2}(z) \times ...?$ Can't be determined $1/ (1 - z)$ $1/ (1 + z)$ $1 - z^{9}$ None of the above

Let $|z| < 1$. Define $M_{n}(z)= \sum_{i=1}^{10} z^{10^{n}(i - 1)}?$ what is $\prod\limits_{i=0}^{\infty} M_{i}(z)= M_{0}(z)\times M_{1}(z) \times M_{2}(z) \t...

makhdoom ghaya

1.2k views

makhdoom ghaya asked Dec 2, 2015

6 votes

1 answer

35

TIFR CSE 2014 | Part A | Question: 7
Consider a sequence of non-negative numbers ${x_{n} : n = 1, 2, . . .}$. Which of the following statements cannot be true? $\sum ^{\infty }_{n=1} x_{n}= \infty $ and $\sum ^{\infty }_{n=1} x_{n}^{2}= \infty$. $\sum ^{\infty }_{n=1} x_{n}= \infty $ ... $\sum ^{\infty }_{n=1} x_{n} < \infty $ and $\sum ^{\infty }_{n=1} x_{n}^{2}= \infty$.

Consider a sequence of non-negative numbers ${x_{n} : n = 1, 2, . . .}$. Which of the following statements cannot be true?$\sum ^{\infty }_{n=1} x_{n}= \infty $ and $\sum...

makhdoom ghaya

975 views

makhdoom ghaya asked Nov 9, 2015

4 votes

3 answers

36

TIFR CSE 2013 | Part A | Question: 15
Let $\DeclareMathOperator{S}{sgn} \S (x)= \begin{cases} +1 & \text{if } x \geq 0 \\ -1 & \text{if } x < 0 \end{cases}$ What is the value of the following summation? $\sum_{i=0}^{50} \S \left ( (2i - 1) (2i - 3) \dots (2i - 99) \right)$ $0$ $-1$ $+1$ $25$ $50$

Let $\DeclareMathOperator{S}{sgn}\S (x)= \begin{cases}+1 & \text{if } x \geq 0 \\-1 & \text{if } x < 0\end{cases}$What is the value of the following summation?$$\sum_{i=0...

makhdoom ghaya

934 views

makhdoom ghaya asked Nov 4, 2015

10 votes

1 answer

37

TIFR CSE 2013 | Part A | Question: 8
Find the sum of the infinite series $\dfrac{1}{1\times 3 \times 5} + \dfrac{1}{3\times 5\times 7} + \dfrac{1}{5\times 7 \times 9} + \dfrac{1}{7\times 9 \times 11} + ......$ $\;\;\infty $ $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{12}\right)$ $\left(\dfrac{1}{14}\right)$

Find the sum of the infinite series $\dfrac{1}{1\times 3 \times 5} + \dfrac{1}{3\times 5\times 7} + \dfrac{1}{5\times 7 \times 9} + \dfrac{1}{7\times 9 \times 11} + .......

makhdoom ghaya

1.3k views

makhdoom ghaya asked Nov 4, 2015

6 votes

1 answer

38

TIFR CSE 2011 | Part A | Question: 8
The sum of the first $n$ terms of the series $1, 11, 111, 1111,\dots,$ is. $\frac{1}{81}\left ( 10^{n+1}-9n-10 \right )$ $\frac{1}{81}\left ( 10^{n}-9n \right )$ $\frac{1}{9}\left ( 10^{n+1}-1\right )$ $\frac{1}{9}\left ( 10^{n+1}-n10^{n}\right )$ None of the above

The sum of the first $n$ terms of the series $1, 11, 111, 1111,\dots,$ is.$\frac{1}{81}\left ( 10^{n+1}-9n-10 \right )$$\frac{1}{81}\left ( 10^{n}-9n \right )$$\frac{1}{9...

makhdoom ghaya

1.0k views

makhdoom ghaya asked Oct 17, 2015

2 votes

3 answers

39

TIFR2010-Maths-A-11
The series $\sum ^{\infty }_{n=1}\frac{(-1)^{n+1}}{\sqrt{n}}$ Converges but not absolutely. Converges absolutely. Diverges. None of the above.

The series $$\sum ^{\infty }_{n=1}\frac{(-1)^{n+1}}{\sqrt{n}}$$ Converges but not absolutely. Converges absolutely. Diverges. None of the above.

Arjun

822 views

Arjun asked Oct 11, 2015

2 votes

2 answers

40

TIFR2010-Maths-A-4
The sum of the series $\frac{1}{1 \cdot 2}+ \frac{1}{2 \cdot 3}+ \frac{1}{3 \cdot 4} + \dots +\frac{1}{100 \cdot 101}$ $\frac{99}{101}$ $\frac{98}{101}$ $\frac{99}{100}$ None of the above

The sum of the series $$\frac{1}{1 \cdot 2}+ \frac{1}{2 \cdot 3}+ \frac{1}{3 \cdot 4} + \dots +\frac{1}{100 \cdot 101}$$$\frac{99}{101}$$\frac{98}{101}$$\frac{99}{100}$No...

makhdoom ghaya

803 views

makhdoom ghaya asked Oct 11, 2015

1 votes

1 answer

41

Series Convergence
I'm having hard time understanding how following series converges ; 1 + 2/5 + 3/5^2 + 4/5^3 + 5/5^4 + ............ infinity

I'm having hard time understanding how following series converges ; 1 + 2/5 + 3/5^2 + 4/5^3 + 5/5^4 + ............ infinity

vishal8492

569 views

vishal8492 asked Aug 22, 2015

12 votes

3 answers

42

GATE CSE 2014 Set 3 | Question: GA-4
Which number does not belong in the series below? $\qquad2, 5, 10, 17, 26, 37, 50, 64$ $17$ $37$ $64$ $26$

Which number does not belong in the series below?$\qquad2, 5, 10, 17, 26, 37, 50, 64$$17$$37$$64$$26$

go_editor

2.7k views

go_editor asked Sep 28, 2014

24 votes

2 answers

43

GATE CSE 2014 Set 2 | Question: GA-5
The value of $\sqrt{12+\sqrt{12+\sqrt{12+\dots}}} $is $3.464$ $3.932$ $4.000$ $4.444$

The value of $\sqrt{12+\sqrt{12+\sqrt{12+\dots}}} $is$3.464$$3.932$$4.000$$4.444$

go_editor

3.2k views

go_editor asked Sep 28, 2014

24 votes

1 answer

44

GATE CSE 2013 | Question: 61
Find the sum of the expression $\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+............+\frac{1}{\sqrt{80}+\sqrt{81}}$ $7$ $8$ $9$ $10$

Find the sum of the expression$\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+............+\frac{1}{\sqrt{80}+\sqrt{81}}$$7$$8$$9$$10...

Arjun

7.6k views

Arjun asked Sep 24, 2014

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