Question:medium
The sum of the series
\( 1 + \frac{1}{2}(1^2 + 2^2) + \frac{1}{3}(1^2 + 2^2 + 3^2) + \dots \)
up to 10 terms is:
The sum of the series
\( 1 + \frac{1}{2}(1^2 + 2^2) + \frac{1}{3}(1^2 + 2^2 + 3^2) + \dots \)
up to 10 terms is:
Show Hint
When the general term \(T_r\) is a polynomial in \(r\), the sum is easily calculated using the standard summation formulas for \(r^2\), \(r\), and constants.
Updated On: Apr 8, 2026
- \(\frac{313}{2}\)
- \(\frac{315}{2}\)
- \(\frac{325}{2}\)
- \(\frac{335}{2}\)
Show Solution
The Correct Option is B
Solution and Explanation
Was this answer helpful?
0
Top Questions on Organic Chemistry
- Product of the following reaction is:
- VITEEE - 2024
- Chemistry
- Organic Chemistry
- The IUPAC name for
- VITEEE - 2024
- Chemistry
- Organic Chemistry
- Which of the following is the major product of the reaction between 1-bromobutane and potassium hydroxide in ethanol?
- VITEEE - 2025
- Chemistry
- Organic Chemistry
- (A) (i) Define a homologous series of carbon compounds.
(ii) Why is the melting and boiling points of \(C_4H_8\) higher than that of \(C_3H_6\) or \(C_2H_4\)?
(iii) Why do we NOT see any gradation in chemical properties of a homologous series compounds?
(iv) Write the name and structures of (i) aldehyde and (ii) ketone with molecular formula \(C_3H_6O\).OR
(B) (i) Write the name and structure of an organic compound ‘X’ having two carbon atoms in its molecule and its name is suffixed with ‘-ol’.
(ii) What happens when ‘X’ is heated with excess concentrated sulphuric acid at 443 K? Write chemical equation for the reaction stating the conditions for the reaction. Also state the role played by concentrated sulphuric acid in the reaction.
(iii) Name and draw the electron dot structure of hydrocarbon produced in the above reaction.- CBSE Class X - 2024
- Science
- Organic Chemistry
- Want to practice more? Try solving extra ecology questions todayView All Questions
