New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Sequences and Series question

2024 · 31 Jan · Shift 1 · Q40

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Sequences and Series
2024 · 31 Jan · Shift 1 · Q40

Sequences and Series question

2024 · 31 Jan · Shift 1 · Q40

JEE MainMathematicsSequences and SeriesMCQ+4 / −1

The sum of the series

\frac{1}{1-3 \cdot 1^2+1^4}+\frac{2}{1-3 \cdot 2^2+2^4}+\frac{3}{1-3 \cdot 3^2+3^4}+\ldots

up to 10 -terms is

A
$\frac{45}{109}$
B
$-\frac{55}{109}$
C
$\frac{55}{109}$
D
$-\frac{45}{109}$

More from Sequences and Series

Let $2^{nd}, 8^{th}$ and $4 4^{th}$ terms of a non-constant A. P. be respectively the $1^{st}, 2^{nd}$ and $3^{rd}$ terms of a G. P. If the first term of the A. P. is 1, then the sum of…2024 · MCQ
Let $a_{1} = 8, a_{2}, a_{3}, \dots, a_{n}$ be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170 , then the product of its middle two terms is .2023 · Numerical
The sum of the common terms of the following three arithmetic progressions. $3, 7, 11, 15, \dots ., 399$ , $2, 5, 8, 11, \dots ., 359$ and $2, 7, 12, 17, \dots ., 197$ , is equal to .2023 · Numerical
If $(20)^{19} + 2 (21) (20)^{18} + 3 (21)^{2} (20)^{17} + \dots + 20 (21)^{19} = k (20)^{19}$ , then $k$ is equal to .2023 · Numerical
Let $S_{K} = \frac{1 + 2 + \dots + K}{K}$ and $\sum_{j = 1}^{n} S_{j}^{2} = \frac{n}{A} (B n^{2} + C n + D)$ , where $A, B, C, D \in N$ and $A$ has least value. Then2023 · MCQ
Let the first term $α$ and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to2023 · MCQ
Let $x_{1}, x_{2}, \dots, x_{100}$ be in an arithmetic progression, with $x_{1} = 2$ and their mean equal to 200 . If $y_{i} = i (x_{i} - i), 1 \leq i \leq 100$ , then the mean of $y_{1}, y_{2}, \dots, y_{100}$ is :2023 · MCQ
Let $a, b, c$ and $d$ be positive real numbers such that $a + b + c + d = 11$ . If the maximum value of $a^{5} b^{3} c^{2} d$ is $3750 β$ , then the value of $β$ is2023 · MCQ