How to simplify any series using a trick

Explore the vast realm of mathematics with this extensive list of keywords, spanning topics such as addition, subtraction, multiplication, division, algebra, geometry, calculus, trigonometry, functions, equations, graphs, probability, statistics, prime numbers, fractions, decimals, percentages, exponents, logarithms, matrices, vectors, complex numbers, sequences, series, limits, derivatives, integrals, differential equations, linear algebra, quadratic equations, arithmetic, geometric shapes, circle, triangle, square, rectangle, parabola, hyperbola, ellipse, congruence, similarity, Pythagorean theorem, area, volume, perimeter, surface area, mean, median, mode, range, standard deviation, variance, probability distribution, normal distribution, binomial distribution, Poisson distribution, exponential distribution, Chi-square distribution, hypothesis testing, confidence intervals, regression analysis, correlation, interpolation, extrapolation, sets, union, intersection, complement, disjoint sets, universal set, subset, Venn diagrams, Cartesian coordinates, polar coordinates, parametric equations, complex plane, eigenvalues, eigenvectors, arithmetic progression, geometric progression, Fibonacci sequence, Pascal's triangle, Newton's method, Riemann sum, Fourier series, Taylor series, vector calculus, partial derivatives, gradient, divergence, curl, Laplace transform, Fourier transform, Z-transform, convolution, matrix multiplication, determinant, inverse matrix, linear regression, nonlinear regression, optimization, critical points, inflection points, sine function, cosine function, tangent function, cosecant function, secant function, cotangent function, arcsin function, arccos function, arctan function, hyperbolic functions, limits at infinity, indefinite integrals, definite integrals, fundamental theorem of calculus, chain rule, product rule, quotient rule, mean value theorem, integration by parts, integration by substitution, polar integration, surface integrals, line integrals, Green's theorem, divergence theorem, Stokes' theorem, Laplace's equation, boundary value ion, Fibonacci heap, golden ratio, Gaussian elimination, LU decomposition, Cholesky decomposition, QR decomposition, singular value decomposition, Gram-Schmidt process, least squares method, matrix factorization, eigen decomposition, power iteration, Jacobi method, Gauss-Seidel method, Newton-Raphson method, bisection method, secant method, regula falsi method, Brent's method, interpolation methods, Lagrange interpolation, Newton interpolation, Hermite interpolation, cubic spline interpolation, Chebyshev interpolation, Neville's algorithm, Neville's theta algorithm, Runge-Kutta methods, Euler method, Heun's method, midpoint method, fourth-order Runge-Kutta method, Adams-Bashforth method, Adams-Moulton method, multistep methods, boundary value methods.
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[Jee_Aspirant_]

GP BE LIKE :- MAIN KYA KARU JOB CHOD DU 😂

[shauryadeb-el]

Math is so interesting when you actually want to do it

[tameen]

This is just the formula for an infinite geometric sequence for anyone wondering. This is the case when |x| < 1.

[AmaanKhan-ztlq]

Just take 1/x common then
A= 1/x ( 1+ 1/x + 1/x²
A= 1/x ( 1+A )
Ax= 1+ A
Ax-A =1
A (x-1) = 1

A = 1/x-1

[Abingusus]

Ur wrong at the very beginning. First you have to prove that this sum has limit and its not infinity. Only after that you can rearrange numbers. If you do it before proving it has limit, you can get any result. Literally theres a theorem that shows if you manipulate with the infinite sum you can get any number depends of what you do

[NotNonaSoft]

Fun fact;
If A = x, then A = Phi, ~1.618

[LambdaFan]

f(x) = x + 1/x
f'(x) = 1 - 1/x^2
Since x has to be positive because it repressents a lenght its minimum is 1 so the minimum value of 1 + 1/x is 2

[kingAmira]

Not for all of time 0>x is - ♾️ but for x>0 is ♾️

[ShivpujanKumarSingh-elor]

Today something hard expression and make it easier I have learnt from this channel❤

[Coding-vmdx]

Need not to do all, just realise that they are in Geometric progression, then the formula will be a/(1-r)
That's easy it is

[umagovindarajan]

Simply use infinite series of GP..
S(♾️)=
a/1-r

[michaelchandriotis]

You can just multiply by x so that Ax = 1 + 1/x + 1/x^2 … so, Ax - A = 1 and A = 1/x-1

[Goldenmemory]

it is direct formula of infinite gp of class 7 aupon 1-r

[Otekos]

I like your videos. However, the animations you choose confuse how you go into the next step. Like they're not based on the operations you do, they seem to be based on the part that looks the most like the other. So I always have to pause the video to understand what's just happened.
Please please sort this out. Coz this is one the greatest content on YouTube

[JiyaBisht-vnfw]

R=1/x

Sum of GP
=first term/1-r

= 1/x/1-1/x

[Pradeeppradeep-cplb]

Yeah my worst nightmare looks just like that

[Juststudy_handle]

Thank you very much because this approach helped me to save my time in my AITS question

[sorooshmj]

the answer when x = 1 is clearly divergant, but if also A = 1/x-1 that means 1/0 is infinity?

[sushmarathi]

Bro why this much complicated
The numbera are in gp just apply the formula and get result

[xristos.l]

That proves that if you divide by zero you grt infinity