Exams
Subjects
Classes
Home
Exams
Mathematics
Sequences and Series
the sum 1 frac 1 2 1 2 2 ...
Question:
medium
The sum \( 1 + \frac{1}{2}(1^2+2^2) + \frac{1}{3}(1^2+2^2+3^2) + \ldots \) upto \(10\) terms is equal to:
JEE Main - 2026
JEE Main
Updated On:
Apr 12, 2026
\(130\)
\(155\)
\( \frac{315}{2} \)
\( \frac{325}{2} \)
Show Solution
The Correct Option is
C
Solution and Explanation
Download Solution in PDF
Was this answer helpful?
0
Top Questions on Sequences and Series
The radius of the base of a cone is increasing at the rate of 3 cm/minute and the altitude is decreasing at the rate of 4 cm/minute. The rate of change of lateral surface when the radius is 7 cm and altitude is 24 cm is:
VITEEE - 2024
Mathematics
Sequences and Series
View Solution
Let \( \alpha = 1^2 + 4^2 + 8^2 + 13^2 + 19^2 + 26^2 + \ldots \) up to 10 terms and \( \beta = \sum_{n=1}^{10} n^4 \). If \( 4\alpha - \beta = 55k + 40 \), then \( k \) is equal to \(\_\_\_\_\_\_\_\_\_\).
JEE Main - 2024
Mathematics
Sequences and Series
View Solution
If \( 8 = 3 + \frac{1}{4}(3 + p) + \frac{1}{4^2}(3 + 2p) + \frac{1}{4^3}(3 + 3p) + \ldots \infty \), then the value of \( p \) is ______.
JEE Main - 2024
Mathematics
Sequences and Series
View Solution
Let 3, a, b, c be in A.P. and 3, a – 1, b + l, c + 9 be in G.P. Then, the arithmetic mean of a, b and c is :
JEE Main - 2024
Mathematics
Sequences and Series
View Solution
Want to practice more? Try solving extra ecology questions today
View All Questions
Questions Asked in JEE Main exam
A long straight wire of circular cross-section (radius \( a \)) is carrying a steady current \( I \). The current \( I \) is uniformly distributed across this cross-section. The magnetic field is:
JEE Main - 2023
VITEEE - 2024
Modern Physics
View Solution
The resistivity (\( \rho \)) of a semiconductor varies with temperature. Which of the following curves represents the correct behavior?
JEE Main - 2023
VITEEE - 2024
Electrostatics
View Solution
Which of the following has a square pyramidal shape?
JEE Main - 2024
Hybridisation
View Solution
Statement I:
Since fluorine is more electronegative than nitrogen, the net dipole moment of NF
3
is greater than NH
3
.
Statement II:
In NH
3
, the orbital dipole due to the lone pair and the dipole moment of NH bonds are in opposite directions, but in NF
3
, the orbital dipole due to the lone pair and the dipole moments of N-F bonds are in the same direction.
In light of the above statements, choose the most appropriate from the options given below:
JEE Main - 2024
Chemical bonding and molecular structure
View Solution
Decreasing order of electron gain enthalpy of the following elements (magnitude only)
Sulphur A, Bromine - B, Fluorine C, Argon D
JEE Main - 2024
Enthalpy change
View Solution