Important Equations

Binomial Expansion

For any value of n, whether positive, negative, integer or non-integer, the value of the nth power of a binomial is given by:
 
 
 In many derivation we are using Binomial expansion to simplify the expression or formula.
 
Important Expansion
1/(1-x)=1+x+x^2+x^3+x^4+x^5+... for -1<x<1  
e^x=1+x+1/2x^2+1/6x^3+1/(24)x^4+... for -infty<x<infty  
ln(1+x)=x-1/2x^2+1/3x^3-1/4x^4+... for -1<x<1  
 
Summation
 
Sum of first N numbers = n(n+1)/2
Sum of squares of N numbers = n(n+1)(2n+1)/6

Comments

Post a Comment

Popular posts from this blog

Rolling Motion made Easy

Image
Q. Many of us we think that Rolling Motion is tough? The answer to the above question is "BIG NO" things are only tough till you understand them completely. So, I am here to guide you on the above topic. Leave comments on any Doubts faced by you recently. When we talk about pure Rotational Motion we imagine a fixed axis about which the all the particles of the Rigid Body are moving in a Circular Motion. Hence if the body moves with angular Velocity ' omega ' (w) than every particle on the periphery will have linear velocity as v =wr ( where r is the radius of the particle from its axis ). In the above Diagram we see 3 figures: 1st figure shows when the body is in pure translational motion only, every particle of the rigid body will have same velocity ( same Direction ) as visible. 2nd figure shows when the body is in pure rotational motion as discussed above particle will have same speed but different velocity about fixed axis O. 3rd figure sh
Read more

Factors affecting of resistances, Combination Of Series and Paralell

Image
 Electric resistance of a conductor (or a wire) depends on the following factors Length of the conductor: - Resistance of a conductor is directly proportional to its length. So, when length of the wire is doubled, its resistance also gets doubled; and if length of the wire is halved its resistance also gets halved. Thus a long wire has more resistance then a short wire. Area of cross-section:- Resistance of a conductor is inversely proportional to its area of cross-section. So, when the area of cross-section of a wire is doubled, its resistance gets halved; and if the area of cross-section of wire is halved then its resistance will get doubled. Thus a thick wire has less resistance and a thin wire has more resistance. 3. Nature of material of conductor:- Electrical resistance of a conductor also depends on the nature of the material of which it is made. For example a copper wire has less resistance then a nichrome wire of same length and area of cross-section. 4
Read more