Question:medium
Sum of \( 1 + \dfrac{1}{2}(1^2 + 2^2) + \dfrac{1}{3}(1^2 + 2^2 + 3^2) + \dots \) up to 10 terms is
Sum of \( 1 + \dfrac{1}{2}(1^2 + 2^2) + \dfrac{1}{3}(1^2 + 2^2 + 3^2) + \dots \) up to 10 terms is
Updated On: Apr 6, 2026
- \( \dfrac{313}{2} \)
- \( \dfrac{315}{2} \)
- 313
- 315
Show Solution
The Correct Option is B
Solution and Explanation
Was this answer helpful?
0
Top Questions on Algebra
- A 3rd order square matrix M satisfies \( M \begin{pmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 2 & 1 \end{pmatrix} = \begin{pmatrix} 0 & 0 & 0 \\ 1 & 1 & 0 \\ 0 & 2 & 1 \end{pmatrix} \) and \( M \begin{pmatrix} 0 & -1 \\ 1 & 2 \\ 2 & 1 \end{pmatrix} = \begin{pmatrix} 1 & 1 \\ 2 & 1 \end{pmatrix} \). If \( M \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \\ 7 \end{pmatrix} \), then \( x + y + z \) is:
- JEE Main - 2026
- Mathematics
- Algebra
- Let \( f(n) = \begin{vmatrix} n & -1 & -5 \\ -2n^2 & 3(2k+1) & 2k+1 \\ -3n^3 & 3k(2k+1) & 3k(k+2)+1 \end{vmatrix} \). If \( \sum_{n=1}^{k} f(n) = 98 \), then find \( k \).
- JEE Main - 2026
- Mathematics
- Algebra
- If the sum of the first 10 terms of the series \( \frac{1}{1 + 4 \cdot 1^4} + \frac{2}{1 + 4 \cdot 2^4} + \frac{3}{1 + 4 \cdot 3^4} + \dots \) is \( \frac{m}{n} \) (where m, n are coprime), then (m + n) is:
- JEE Main - 2026
- Mathematics
- Algebra
- If \( \alpha, \beta \) are the roots of the equation \( x^2 - 4x + p = 0 \) and \( \gamma, \delta \) are the roots of the equation \( x^2 - x + q = 0 \). When \( \alpha, \beta, \gamma, \delta \) form a G.P. with positive common ratio, then the value of \( (p + q) \) equals:
- JEE Main - 2026
- Mathematics
- Algebra
- Want to practice more? Try solving extra ecology questions todayView All Questions
