List of top Mathematics Questions on Sequences and Series asked in JEE Main

The sum $ 1 + \frac{1 + 3}{2!} + \frac{1 + 3 + 5}{3!} + \frac{1 + 3 + 5 + 7}{4!} + ... $ upto $ \infty $ terms, is equal to

If $ \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + ... \infty = \frac{\pi^4}{90}, $ $ \frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + ... \infty = \alpha, $ $ \frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + ... \infty = \beta, $ then $ \frac{\alpha}{\beta} $ is equal to:

Let $ a_1, a_2, a_3, ... $ be a G.P. of increasing positive numbers. If $ a_3 a_5 = 729 $ and $ a_2 + a_4 = \frac{111}{4} $, then $ 24(a_1 + a_2 + a_3) $ is equal to

The sum 1 + 3 + 11 + 25 + 45 + 71 + ... upto 20 terms, is equal to

1 + 3 + $5^2$ + 7 + $9^2$ + $\ldots$ upto 40 terms is equal to

Let $A = \{1, 6, 11, 16, \ldots\}$ and $B = \{9, 16, 23, 30, \ldots\}$ be the sets consisting of the first 2025 terms of two arithmetic progressions. Then $n(A \cup B)$ is

Let $ x_1, x_2, x_3, x_4 $ be in a geometric progression. If 2, 7, 9, 5 are subtracted respectively from $ x_1, x_2, x_3, x_4 $, then the resulting numbers are in an arithmetic progression. Then the value of $ \frac{1}{24} (x_1 x_2 x_3 x_4) $ is:

Let the points $ \left( \frac{11}{2}, \alpha \right) $ lie on or inside the triangle with sides $ x + y = 11 $, $ x + 2y = 16 $, and $ 2x + 3y = 29 $. Then the product of the smallest and the largest values of $ \alpha $ is equal to:

Let $ a_1, a_2, a_3, \dots $ be a G.P. of increasing positive terms. If $ a_1 a_5 = 28 $ and $ a_2 + a_4 = 29 $, then the value of $ a_6 $ is equal to:

Let $ a_1, a_2, a_3, \ldots $ be in an A.P. such that \[ \sum_{k=1}^{12} a_{2k-1} = -\frac{72}{5} a_1, \quad a_1 \neq 0. \] If \[ \sum_{k=1}^{n} a_k = 0, \] then $ n $ is:

Let $ P_n = \alpha^n + \beta^n $, $ P_{10} = 123 $, $ P_9 = 76 $, $ P_8 = 47 $, and $ P_1 = 1 $. The quadratic equation whose roots are $ \frac{1}{\alpha} $ and $ \frac{1}{\beta} $ is:

Let $ \langle a_n \rangle $ be a sequence such that $ a_0 = 0 $, $ a_1 = \frac{1}{2} $, and $ 2a_{n+2} = 5a_{n+1} - 3a_n $.n= 0,1,2,3.... Then $ \sum_{k=1}^{100} a_k $ is equal to:

Given: $ \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \cdots = \frac{\pi^4}{90}, $ $ \frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + \cdots = \alpha, $ $ \frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + \cdots = \beta $ Find the value of $ \frac{\alpha}{\beta} $.

Let the area of the region $$ \{(x, y) : 2y \leq x^2 + 3, \quad y + |x| \leq 3, \quad y \geq |x-1|\} $$ be $ A $. Then $ 6A $ is equal to:

The total number of 10-digit sequences formed by only $ \{0, 1, 2\} $, where 1 should be used at least 5 times and 2 should be used exactly three times, is:

Let $ a_1, a_2, a_3, \dots $ be an A.P. and $ \sum_{k=1}^{12} a_{2k-1} = -\frac{72}{5} a_1 $ and $ \sum_{k=1}^{n} a_k = 0 $. Then the value of $ n $ is:

Let $ S = \mathbb{N} \cup \{0\} $. Define a relation $ R $ from $ S $ to $ \mathbb{R} $ by: \[ R = \left\{ (x, y) : \log_e y = x \log_e \left(\frac{2}{5}\right), x \in S, y \in \mathbb{R} \right\}. \] Then, the sum of all the elements in the range of $ R $ is equal to:

Let the points $ \left( \frac{11}{2}, \alpha \right) $ lie on or inside the triangle with sides $ x + y = 11 $, $ x + 2y = 16 $, and $ 2x + 3y = 29 $. Then the product of the smallest and the largest values of $ \alpha $ is equal to:

Let $ \langle a_n \rangle $ be a sequence such that $ a_0 = 0 $, $ a_1 = \frac{1}{2} $, and $ 2a_{n+2} = 5a_{n+1} - 3a_n $.n= 0,1,2,3.... Then $ \sum_{k=1}^{100} a_k $ is equal to:

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 $\_\_\_\_\_\_\_\_\_$.

Let the positive integers be written in the form :