Recent questions tagged number-series

1
Consider the series $\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{8}+\frac{1}{9}-\frac{1}{16}+\frac{1}{32}+\frac{1}{27}-\frac{1}{64}+\ldots.$ The sum of the infinite series above is$:$ $\infty$ $\frac{5}{6}$ $\frac{1}{2}$ $0$
1 vote
2
Look at this series: $25, 25, 37, 37, \dots , 51, ….$. What number should fill the blank? $51$ $39$ $23$ $25$
1 vote
3
Look at this series: $5000, 1001, 201, 41, \dots$ What number should come next? $9$ $10$ $11$ $42$
4
Let $T$ be the set of integers $\{3,11,19,27, ..... , 451, 459, 467\}$ and $S$ be a subset of $T$ such that the sum of no two elements of $S$ is $470$. The maximum possible number of elements in $S$ is ? $31$ $28$ $29$ $30$ Answer is given as c. 29. But as per my calculations the answer has to be d.30. Let me know if my answer is correct.
5
The sum of an infinite geometric series of real numbers is $14$, and the sum of the cubes of the terms of this series is $392$. Then the first term of the series is $-14$ $10$ $7$ $-5$
6
What is the value of $1 + \dfrac{1}{4} + \dfrac{1}{16} + \dfrac{1}{64} + \dfrac{1}{256} + .............?$ $2$ $\dfrac{7}{4}$ $\dfrac{3}{2}$ $\dfrac{4}{3}$
1 vote
7
Consider a sequence of numbers $a_1, a_2, a_3, \dots , a_n$ where $a_n = \frac{1}{n}-\frac{1}{n+2}$, for each integer $n>0$. Whart is the sum of the first 50 terms? $\left( 1+ \frac{1}{2} \right) - \frac{1}{50}$ $\left( 1+ \frac{1}{2} \right) + \frac{1}{50}$ $\left( 1+ \frac{1}{2} \right) - \left( \frac{1}{51} + \frac{1}{52} \right)$ $1 - \left( \frac{1}{51} + \frac{1}{52} \right)$
1 vote
8
value of 1/3 + 1/15 + 1/35 +............................+1/9999 a)100/101 b)50/101 c)100/51 d)50/51
1 vote
9
196 : 169 : 81 : ? (a) 64 (b) 72 (c) 100 (d) None Is a option correct here or do we need to look at the the square root of them for some other relation 14,13,9 .If none was not there i would have selected a only.
1 vote
10
Find next number in series? 15,10,5,150,16,12,4,192,20,15,5,....?
11
1 vote
12
If m and n are whole numbers and $m^{n} = 125$ then the value of $(m-5)^{n+1}=?$
13
0, 11, 36, 81, ____?
14
Fill in the missing number in the series. $2$ $3$ $6$ $15$ ___ $157.5$ $630$
15
What is the next number in the series? $12$ $35$ $81$ $173$ $357$ _______.
16
Find the next term in the sequence: $7G, 11K, 13M$, _________. $15Q$ $17Q$ $15P$ $17P$
17
The next term in the series $81, 54, 36, 24,\dots$ is_________.
18
Find the sum to $'n'$ terms of the series $10+84+734+\dots$ $\frac{9(9^n+1)}{10} +1$ $\frac{9(9^n-1)}{8} +1$ $\frac{9(9^n-1)}{8} +n$ $\frac{9(9^n-1)}{8} +n^2$
19
Let $|z| < 1$. Define $M_{n}(z)= \sum_{i=1}^{10} z^{10^{n}(i - 1)}?$ what is $\prod_{i=0}^{\infty} M_{i}(z)= M_{0}(z)\times M_{1}(z) \times M_{2}(z) \times ...?$ Can't be determined. $1/ (1 - z)$ $1/ (1 + z)$ $1 - z^{9}$ None of the above.
20
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 $\sum ^{\infty }_{n=1} x_{n}^{2}= \infty$.
21
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? $\sum_{i=0}^{50} \S \left ( (2i - 1) (2i - 3) \dots (2i - 99) \right)$ $0$ $-1$ $+1$ $25$ $50$
22
Find the sum of the infinite series $\dfrac{1}{1\times 3 \times 5} + \dfrac{1}{3\times 5\times 7} + \dfrac{1}{5\times 7 \times 9} + \dfrac{1}{7\times 9 \times 11} + ......$ $\;\;\infty$ $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{12}\right)$ $\left(\dfrac{1}{14}\right)$
23
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.
24
The series $\sum ^{\infty }_{n=1}\frac{(-1)^{n+1}}{\sqrt{n}}$ Converges but not absolutely. Converges absolutely. Diverges. None of the above.
25
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
1 vote
Which number does not belong in the series below? $\qquad2, 5, 10, 17, 26, 37, 50, 64$ $17$ $37$ $64$ $26$
The value of $\sqrt{12+\sqrt{12+\sqrt{12+\dots}}}$is $3.464$ $3.932$ $4.000$ $4.444$