What is the co-efficient of $x^2$ in the expansion of $\left(x+\frac{1}{x^2}\right)^{20}$?
The correct answer should be $605\frac{5}{8}$.
2026-04-04 21:02:46.1775336566
What is the co-efficient of $x^2$ in the expansion of $(x+\frac{1}{x^2})^{20}$?
67 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
2
There are 2 best solutions below
Related Questions in COMBINATORICS
- Using only the digits 2,3,9, how many six-digit numbers can be formed which are divisible by 6?
- The function $f(x)=$ ${b^mx^m}\over(1-bx)^{m+1}$ is a generating function of the sequence $\{a_n\}$. Find the coefficient of $x^n$
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Hard combinatorial identity: $\sum_{l=0}^p(-1)^l\binom{2l}{l}\binom{k}{p-l}\binom{2k+2l-2p}{k+l-p}^{-1}=4^p\binom{k-1}{p}\binom{2k}{k}^{-1}$
- Algebraic step including finite sum and binomial coefficient
- nth letter of lexicographically ordered substrings
- Count of possible money splits
- Covering vector space over finite field by subspaces
- A certain partition of 28
- Counting argument proof or inductive proof of $F_1 {n \choose1}+...+F_n {n \choose n} = F_{2n}$ where $F_i$ are Fibonacci
Related Questions in EXPONENTIAL-FUNCTION
- How to solve the exponential equation $e^{a+bx}+e^{c+dx}=1$?
- derive the expectation of exponential function $e^{-\left\Vert \mathbf{x} - V\mathbf{x}+\mathbf{a}\right\Vert^2}$ or its upper bound
- How do you calculate the horizontal asymptote for a declining exponential?
- Intersection points of $2^x$ and $x^2$
- Integrate exponential over shifted square root
- Unusual Logarithm Problem
- $f'(x)=af(x) \Rightarrow f(x)=e^{ax} f(0)$
- How long will it take the average person to finish a test with $X$ questions.
- The equation $e^{x^3-x} - 2 = 0$ has solutions...
- Solve for the value of k for $(1+\frac{e^k}{e^k+1})^n$
Related Questions in BINOMIAL-COEFFICIENTS
- Newton binomial expansion
- Justify an approximation of $\sum_{n=1}^\infty G_n/\binom{\frac{n}{2}+\frac{1}{2}}{\frac{n}{2}}$, where $G_n$ denotes the Gregory coefficients
- Solving an equation involving binomial coefficients
- Asymptotics for partial sum of product of binomial coefficients
- What is wrong with this proof about a sum of binomial coefficients?
- Find sum of nasty series containing Binomial Coefficients
- Alternating Binomial Series Summation.
- $x+\frac{1}{x}$ is an integer
- Finding value of $S-T$ in $2$ binomial sum.
- how to reduce $(1-\alpha)^{T-i}$ into a sum
Related Questions in FRACTIONS
- Can we find integers $x$ and $y$ such that $f,g,h$ are strictely positive integers
- How would I simplify this fraction easily?
- Decimal expansion of $\frac{1}{p}$: what is its period?
- To find the Modulus of a complex number
- Tan of difference of two angles given as sum of sines and cosines
- Positive Integer values of a fraction
- What is the range of the function $f(x)=\frac{4x(x^2+1)}{x^2+(x^2+1)^2}$?
- In resticted domain , Applying the Cauchy-Schwarz's inequality
- for $x,y,z\ge 0$, $x+y+z=2$, prove $\frac{x}{1+y^2}+\frac{y}{1+z^2}+\frac{z}{1+x^2}\ge\frac{18}{13}$
- Interesting inequalities
Related Questions in BINOMIAL-THEOREM
- Prove $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$ using binomial and induction
- Use the binomial theorem to prove that for $n$ a positive integer the following holds
- Proving the binomial series for all real (complex) n using Taylor series
- Find sum of nasty series containing Binomial Coefficients
- Value of $a_2+a_6+a_{10}+\cdots+a_{42}$
- Definite sum for $(1+a)^n$
- How to prove $\sum_{r=1}^{n} r^{2}\binom {n} {r} = n(n+1)2^{n-2}$?
- Binomial Theorem Question $1+(1+x)+(1+x)^2+\dots+(1+x)^n$
- Distinct terms in a binomial expansion
- Limit of a sequence (binomial series and generating function for Catalan)
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
It's $$\frac{(x^3+1)^{20}}{x^{40}}$$ and since $x^{42}=(x^3)^{14}$, we get the answer: $\binom{20}{14}$.