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An arithematic progression has terms in a sequence such that the difference between any two consecutive terms is a constant and is given by a common difference, say, d. If first term in the progression is a,...

The matrix is singular. No inverse matrix. Geometrically: No unique point of intersection of planes, Either no common point, a line of intersection or the three planes coincide. Alegebriacally: No unique sol...

There are many methods to check it, but the the most useful is: By comparison: if we find a series whose terms are greater than the given ones which is known to be convergent (an armonic series for example),...

Sometimes it would be enough to factorise the polynomials (in case the limit we are trying to compute is writen in terms of polynomials) and eliminate common factors in the quotient. However, most of them ca...

There are, mainly, three ways of doing it easily: Substitution: It consists in modifying one of the equations in such a way that x is expressed in terms of y (or y in terms of x) and then substitute that exp...