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Sequences and Series

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2025
The value of $\mathop {\lim }\limits_{n \to \infty } \left( {\sum\limits_{k = 1}^n {\frac{{{k^3} + 6{k^2} + 11k + 5}}{{(k + 3)!}}}} \right)$ is:
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let ${{\rm{T}}_{\rm{r}}}$ be the ${{\rm{r}}^{{\rm{th }}}}$ term of an A.P. If for some ${\rm{m}},{{\rm{T}}_{\rm{m}}} = \frac{1}{{25}},\;{{\rm{T}}_{25}} = \frac{1}{{20}}$ , and $...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let $\left\langle {{a_{\rm{n}}}} \right\rangle $ be a sequence such that ${a_0} = 0,{a_1} = \frac{1}{2}$ and $...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Let ${S_n} = \frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + \ldots $ upto $n$ terms. If the sum of the first six terms of...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
If $\sum_{r=1}^n T_r=\frac{(2 n-1)(2 n+1)(2 n+3)(2 n+5)}{64}, then {\lim _{n \rightarrow \infty} \sum_{r=1}^n\left(\frac{1}{T_r}\right)}$ is equal to :
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Suppose that the number of terms in an A.P. is $2 k, k \in \mathbf{N}$. If the sum of all odd terms of the A.P....
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let ${{a}_{1}},{{a}_{2}},{{a}_{3}},\ldots $ be a G.P. of increasing positive terms. If ${{a}_{1}}{{a}_{5}}=28$ and ${{a}_{2}}+{{a}_{4}}=29$, then ${{a}_{6}}$ is equal to :
JEE Main Mathematics Easy
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