Logs Change of Base Formula | Logarithm

Here you will learn logs change of base formula in logarithm and logarithmic inequalities with example. Let’s begin – Logs Change of Base Formula – Base Changing Theorem It can be stated as “quotient of the algorithm of two numbers is independent of their common base.” Symbolically, \(log_b m\) = \(log_a m \over log_a b\), …

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Total Number of Combinations | Permutation and Combination

Here you will learn how to find total number of combinations and distribution of distinct objects and alike objects. Let’s begin – Total Number of Combinations (a)  Given n different objects, the number of ways of selecting at least one of them is, \(^{n}C_1\) + \(^{n}C_2\) + \(^{n}C_3\) +…….+ \(^{n}C_n\) This can also be stated …

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Dearrangement Formula | Permutations of Alike Objects

Here you will learn dearrangement formula and permutation of alike objects with example. Let’s begin – Dearrangement Formula There are n letters and n corresponding envelopes. The number of ways in which letters can be placed in the envelopes (one letter in each envelope) so that no letter is placed in correct envelope is n![1 …

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Sum of GP Series Formula | Properties of GP

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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Formula for Sum of AP Series | Properties of AP

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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Formula for Circumcenter of a Triangle | Incenter of Triangle

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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Centroid in a Triangle – Formula and Example

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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