Question:
Let \(a_n=\sin(\frac{1}{n^3})\) and \(b_n=\sin(\frac{1}{n})\) for n ∈ \(\N\). Then
Let \(a_n=\sin(\frac{1}{n^3})\) and \(b_n=\sin(\frac{1}{n})\) for n ∈ \(\N\). Then
Updated On: Oct 1, 2024
- both \(\sum\limits_{n=1}^{\infin}a_n\) and \(\sum\limits_{n=1}^{\infin}b_n\) are convergent
- \(\sum\limits_{n=1}^{\infin}a_n\) is convergent \(\sum\limits_{n=1}^{\infin}b_n\) is NOT convergent
- \(\sum\limits_{n=1}^{\infin}a_n\) is NOT convergent \(\sum\limits_{n=1}^{\infin}b_n\) is convergent
- both \(\sum\limits_{n=1}^{\infin}a_n\) and \(\sum\limits_{n=1}^{\infin}b_n\) are NOT convergent
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct option is (B) : \(\sum\limits_{n=1}^{\infin}a_n\) is convergent \(\sum\limits_{n=1}^{\infin}b_n\) is NOT convergent.
Was this answer helpful?
0
0
Top Questions on Sequences and Series
- For n ≥ 3, let a regular n-sided polygon Pn be circumscribed by a circle of radius Rn and let rn be the radius of the circle inscribed in Pn. Then
\(\lim\limits_{n \rightarrow \infin}(\frac{R_n}{r_n})^{n^2}\)
equals- IIT JAM MA - 2024
- Real Analysis
- Sequences and Series
- For $x \geq 0$, the least value of $K$, for which $4^{1+x}, 4^{1-x}, \frac{K}{2}, 16^{x}, 16^{-x}$ are three consecutive terms of an A.P. is equal to:
- JEE Main - 2024
- Mathematics
- Sequences and Series
- Let the first three terms \(2\), \(p\), and \(q\), with \(q \neq 2\), of a G.P. be respectively the \(7^\text{th}\), \(8^\text{th}\), and \(13^\text{th}\) terms of an A.P. If the \(5^\text{th}\) term of the G.P. is the \(n^\text{th}\) term of the A.P., then \(n\) is equal to:
- JEE Main - 2024
- Mathematics
- Sequences and Series
- The value of \[ \frac{1 \times 2^2 + 2 \times 3^2 + \dots + 100 \times (101)^2}{1^2 \times 2 + 2^2 \times 3 + \dots + 100^2 \times 101} \] is:
- JEE Main - 2024
- Mathematics
- Sequences and Series
- Let three real numbers a,b,c be in arithmetic progression and a + 1, b, c + 3 be in geometric progression. If a>10 and the arithmetic mean of a,b and c is 8, then the cube of the geometric mean of a,b and c is
- JEE Main - 2024
- Mathematics
- Sequences and Series
View More Questions
Questions Asked in IIT JAM MA exam
- Consider the function f: ℝ → ℝ given by f(x) = x3 - 4x2 + 4x - 6.
For c ∈ ℝ, let
\(S(c)=\left\{x \in \R : f(x)=c\right\}\)
and |S(c)| denote the number of elements in S(c). Then, the value of
|S(-7)| + |S(-5)| + |S(3)|
equals _________- IIT JAM MA - 2024
- Functions of One Real Variable
- For a > b > 0, consider
\(D=\left\{(x,y,z) \in \R^3 :x^2+y^2+z^2 \le a^2\ \text{and } x^2+y^2 \ge b^2\right\}.\)
Then, the surface area of the boundary of the solid D is- IIT JAM MA - 2024
- Functions of Two or Three Real Variables
- Consider the 4 × 4 matrix
\(M = \begin{pmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 1 & 2 \\ 2 & 1 & 0 & 1 \\ 3 & 2 & 1 & 0 \end{pmatrix}\)
If ai,j denotes the (i, j)th entry of M-1 , then a4,1 equals __________ (rounded off to two decimal places).- IIT JAM MA - 2024
- Matrices
- Let
S = {f: ℝ → ℝ ∶ f is a polynomial and f(f(x)) = (f(x))2024 for x ∈ ℝ}.
Then, the number of elements in S is _____________- IIT JAM MA - 2024
- Functions of One Real Variable
- The value of
\(\lim\limits_{t→\infin}\left((\log(t^2+\frac{1}{t^2}))^{-1} \int\limits_{1}^{\pi t} \frac{\sin^25x}{x}dx\right)\)
equals ___________ (rounded off to two decimal places).- IIT JAM MA - 2024
- Integral Calculus
View More Questions