Question:
If the sum of the series \(\left(\frac{1}{2}-\frac{1}{3}\right) + \left(\frac{1}{2^2}-\frac{1}{2·3} + \frac{1}{3^2}\right) + \left(\frac{1}{2^2}-\frac{1}{2^2·3} + \frac{1}{2·3^2} - \frac{1}{3^3}\right) + \left(\frac{1}{2^4}-\frac{1}{2^3·3} + \frac{1}{2^2·3^2} - \frac{1}{2·3^3} + \frac{1}{3^4}\right) + ........ \)
is \(\frac{α}{β}\) , where α and β are co-prime, then α+3β is equal to ________
If the sum of the series \(\left(\frac{1}{2}-\frac{1}{3}\right) + \left(\frac{1}{2^2}-\frac{1}{2·3} + \frac{1}{3^2}\right) + \left(\frac{1}{2^2}-\frac{1}{2^2·3} + \frac{1}{2·3^2} - \frac{1}{3^3}\right) + \left(\frac{1}{2^4}-\frac{1}{2^3·3} + \frac{1}{2^2·3^2} - \frac{1}{2·3^3} + \frac{1}{3^4}\right) + ........ \)
is \(\frac{α}{β}\) , where α and β are co-prime, then α+3β is equal to ________
is \(\frac{α}{β}\) , where α and β are co-prime, then α+3β is equal to ________
Updated On: Mar 21, 2025
Hide Solution
Verified By Collegedunia
Correct Answer: 7
Solution and Explanation
Was this answer helpful?
0
4
Top Questions on Series
- The value of \[ \lim_{n \to \infty} \sum_{k=1}^{n} \frac{k^3 + 6k^2 + 11k + 5}{(k + 3)!} \] is:
- In the expansion of $(1 + x)^n$, $\frac{{}^nC_1}{{}^nC_0} + 2 \cdot \frac{{}^nC_2}{{}^nC_1} + 3 \cdot \frac{{}^nC_3}{{}^nC_2} + \dots + n \cdot \frac{{}^nC_n}{{}^nC_{n-1}}$ is equal to:
- If \( \sum_{k=1}^{n} k(k+1)(k-1) = pn^4 + qn^3 + tn^2 + sn \), where \( p, q, t, s \) are constants, then the value of \( s \) is equal to:
- There are four numbers of which the first three are in GP and the last three are in AP, whose common difference is 6. If the first and the last numbers are equal, then the two other numbers are:
- The sum of the infinite series \(1 + \frac{5}{6} + \frac{12}{6^2} + \frac{22}{6^3} + \frac{35}{6^4} + \dots\) is equal to:
View More Questions
Questions Asked in JEE Main exam
- In YDSE, light of intensity \( 4I \) and \( 9I \) passes through two slits respectively. Difference of maximum and minimum intensity of interference pattern is:
- JEE Main - 2025
- Wave optics
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
- JEE Main - 2025
- Differential Equations
Find the IUPAC name of the compound.
- JEE Main - 2025
- Aromaticity & chemistry of aromatic compounds
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32
- JEE Main - 2025
- Limits and Exponential Functions
- The integral \[ \int_0^\pi \frac{8x}{4\cos^2 x + \sin^2 x} \, dx \text{ is equal to:} \]
- JEE Main - 2025
- Trigonometric Functions
View More Questions