New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Sequences and Series question

2025 · 2 Apr · Shift 2 · Q48

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

PYQ Library
JEE Main
Mathematics
Sequences and Series
2025 · 2 Apr · Shift 2 · Q48

Sequences and Series question

2025 · 2 Apr · Shift 2 · Q48

JEE MainMathematicsSequences and SeriesNumerical+4 / −1

If the sum of the first 10 terms of the series

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

. is

\frac{\mathrm{m}}{\mathrm{n}}

, where

\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1

, then

\mathrm{m}+\mathrm{n}

is equal to

\underline{\hspace{2cm}}

Numerical answer

More from Sequences and Series

Let $a_{1}, a_{2}, a_{3}, \dots$ . 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 to2025 · MCQ
The sum $1 + 3 + 11 + 25 + 45 + 71 + \dots$ upto 20 terms, is equal to2025 · MCQ
The sum $1 + \frac{1 + 3}{2 !} + \frac{1 + 3 + 5}{3 !} + \frac{1 + 3 + 5 + 7}{4 !} + \dots$ upto $\infty$ terms, is equal to2025 · MCQ
Let $A = {1, 6, 11, 16, \dots}$ and $B = {9, 16, 23, 30, \dots}$ be the sets consisting of the first 2025 terms of two arithmetic progressions. Then $n (A \cup B)$ is2025 · MCQ
$1 + 3 + 5^{2} + 7 + 9^{2} + \dots$ upto 40 terms is equal to2025 · MCQ
If the sum of the first 20 terms of the series $\frac{4 \cdot 1}{4 + 3 \cdot 1 ^{2} + 1 ^{4}} + \frac{4 \cdot 2}{4 + 3 \cdot 2 ^{2} + 2 ^{4}} + \frac{4 \cdot 3}{4 + 3 \cdot 3 ^{2} + 3 ^{4}} + \frac{4 \cdot 4}{4 + 3 \cdot 4 ^{2} + 4 ^{4}} + \dots \cdot$ is…2025 · MCQ
Consider two sets A and B, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the elements of B be 36 and $q$ respectively. Let d and D be the…2025 · MCQ
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 $\frac{1}{24} (x_{1} x_{2} x_{3} x_{4})$ …2025 · MCQ