Question:
The value of the sum of 10 term of the series
\(S_{10}=\frac{1}{2^2-1}+\frac{1}{4^2-1}+\frac{1}{6^2-1}+...\)
The value of the sum of 10 term of the series
\(S_{10}=\frac{1}{2^2-1}+\frac{1}{4^2-1}+\frac{1}{6^2-1}+...\)
\(S_{10}=\frac{1}{2^2-1}+\frac{1}{4^2-1}+\frac{1}{6^2-1}+...\)
Updated On: Sep 12, 2024
- \(\frac{11}{21}\)
- \(\frac{9}{10}\)
- \(\frac{21}{10}\)
- \(\frac{10}{21}\)
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct option is (D):\(\frac{10}{21}\).
Was this answer helpful?
0
0
Top Questions on Principle of Mathematical Induction
- Sum of the series \(\frac {1}{1-3.1^2+1^4}+\frac {2}{1-3.2^2+2^4}+\frac {3}{1-3.3^2+3^4}\) upto \(10\) terms is _____ .
- JEE Main - 2024
- Mathematics
- Principle of Mathematical Induction
- Let \(P(n)=3^{2n+1}+2^{n+2}\) where n∈N. Then
- WBJEE - 2023
- Mathematics
- Principle of Mathematical Induction
- Match List I with List II
LIST I LIST II A. Series \(\displaystyle\sum_{n=1}^{∞} \frac{1}{n^\frac{3}{2}}\) is I. Monotone and
convergent bothB. Series \(\displaystyle\sum_{n=1}^{∞} \frac{3^n}{n^2}\) is II. \(e^{-2}\) C. \(\lim\limits_{n \to \infty} (\frac{n+1}{n+2})^{2n+1}\) III. Divergent to ∞ D. sequence \(x_n=1+\frac{1}{2!}+\frac{1}{3!}+…\frac{1}{n!}\) for n∈N IV. Convergent Choose the correct answer from the options given below:- CUET (PG) - 2023
- Mathematics
- Principle of Mathematical Induction
- The value of \(\lim\limits_{n \to \infty} \frac{1}{n} [1+2^{\frac{1}{2}}+3^{\frac{1}{3}}+...n^{\frac{1}{n}}]\) is
- CUET (PG) - 2023
- Mathematics
- Principle of Mathematical Induction
- The infinite series \(\displaystyle\sum_{n=1}^{∞} (1+\frac{1}{n})^{-n^2}\) is:
- CUET (PG) - 2023
- Mathematics
- Principle of Mathematical Induction
View More Questions
Questions Asked in CUET exam
- A molecule X associates in a given solvent as per the following equation:
X ⇌ (X)n
For a given concentration of X, the van’t Hoff factor was found to be 0.80 and the
fraction of associated molecules was 0.3. The correct value of ‘n’ is:- CUET (UG) - 2024
- Solutions
- Who devised the concept of Intelligence Quotient (IQ)?
- CUET (UG) - 2024
- Psychological attributes
- Two pipes A and B can fill a tank in 32 minutes and 48 minutes respectively. If both the pipes are opened simultaneously, after how much time B should be turned off so that the tank is full in 20 minutes?
- CUET (UG) - 2024
- Time and Work
- If \(A = \begin{bmatrix} 3 & 2 \\ -1 & 1 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} -1 & 0 \\ 2 & 5 \\ 3 & 4 \end{bmatrix},\)then \((BA)^T\) is equal to:
- CUET (UG) - 2024
- Matrices
- The spin-only magnetic moment of Hexacyanomanganate(II) ion is.........BM
- CUET (UG) - 2024
- Magnetic moment
View More Questions