Here you will learn what is harmonic progression (hp) and sum of harmonic progression (hp series). Let’s begin – Sum of Harmonic Progression A sequence is said to be in H.P. if the reciprocal of its terms are in A.P. If the sequence \(a_1\) + \(a_2\) + \(a_3\) + ……… + \(a_n\) is an HP […]
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Here you will learn what is geometric progression (gp) and sum of gp series formula and properties of gp. Let’s begin – Sum of GP Series Formula G.P. is a sequence of non zero numbers each of the succeeding term is equal to the preceding term multiplied by a constant. Thus in GP the ratio
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Here, you will learn what is arithmetic progression (ap) and formula for sum of ap series and properties of ap. Let’s begin – The indicated sum of the terms of a sequence. In the case of a finite sequence \(a_1\), \(a_2\), \(a_3\),………,\(a_n\) the corresponding series is \(a_1\) + \(a_2\) + \(a_3\) + ……… + \(a_n\)
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Here you will learn formula for orthocenter in a triangle, ex-centers and equation of locus of a point. Let’s begin – Orthocenter in a Triangle It is the point of intersection of perpendiculars drawn from the vertices on the opposite sides of a triangle and it can be obtained by solving the equation of any
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Here, you will learn formula for circumcenter of a triangle and formula for incenter of a triangle. Let’s begin – Formula for Circumcenter of a Triangle It is the point of intersection of perpendicular bisectors of the sides of a triangle. If O is the circumcenter of any triangle ABC, then \(OA^2\) = \(OB^2\) =
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Here you will learn formula for centroid of triangle and how to find centroid in a triangle with example. Let’s begin – Centroid in a Triangle If A(\(x_1,y_1\)), B(\(x_2,y_2\)) and C(\(x_3,y_3\)) are vertices of any triangle ABC, then The centroid is the point of the intersection of the medians(line joining the mid-point of sides and
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Here, you will learn what is the section formula and distance formula and and applications of distance formula. Let’s begin – Section Formula – for internal and external division The co-ordinates of a point dividing a line joining the points P(\(x_1,y_1\)) and Q(\(x_2,y_2\)) in the ratio m : n is given by : (a) for
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Here, you will learn formulas for definite integrals and properties of definite integrals with examples. Let’s begin – A definite integral is denoted by \(\int_{a}^{b}\) f(x)dx which represent the algebraic area bounded by the curve y = f(x), the ordinates x = a, x = b and the x-axis. Properties and Formulas for Definite Integrals
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Here, you will learn state polygon law of vector addition, subtraction of vectors and multiplication of vector by scalars. Let’s begin – Polygon law of vector Addition (Addition of more than two vectors) Addition of more than two vectors is found to be by repetition of triangle law. Suppose we have to find the sum
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Here, you will learn triangle law of addition of vectors and parallelogram law of addition of vectors and properties of vector addition. Let’s begin – Addition of Vectors The vectors have magnitude as well as direction, therefore their addition is different than addition of real numbers. Let \(\vec{a}\) and \(\vec{b}\) be two vectors in a
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