logarithmic series

Logarithmic Series - If x is a real number such that |x|<1, then the series is called the logarithmic series. It can be proved mathematically that this logarithmic series has the sum equal to log(1 + x). If x is a re..

If x is a real number such that |x|<1, then the series is called the logarithmic series. It can be proved mathematically that this logarithmic series has the sum equal to log(1 + x..

The following are the Some Particular Logarithmic Series: ..

Particular Logarithmic Series - For any number x such that |x|<1. i) For number x:|x|<1, we have |-x|=|x|<1. iii) It can be proved mathematically that the logarithmic series (1) is true even whe..

For any number x such that |x|<1. i) For number x:|x|<1, we have |-x|=|x|<1. iii) It can be proved mathematically that the logarithmic series (1) is true even when x=1..

2 < e < 3 The value of e rounded off to four decimal places is 2.7183. For complex numbers x,y, we have e x + y = e x y y . For any rational number x, the sum, e x , of the series ..

The sum of the infinite series 1 + 1/1! + 1/2! + 1/3! + 1/4! + ... is called the exponential number. If x is any complex number then the series is called the exponential series. It can be proved mathematically that this exponential series has ..

In this chapter, we shall study two series known as the Exponential series and Logarithmic series. In our discussion, we shall make use of mathematical tools like formula for sum of an infinite G.P., combinatorial coefficient..

T he terms in log(1 + x) carry alternatively positive and negative signs. The terms in log(1 + x) do not involve factorials as in the exponential series. ..

Different forms of numbers Scientific notation, square roots, exponents, radicals, absolute value, factorial, logarithms Properties of numbers Estimation of solutions Sequences and series Proportionality/direct variation, exponential/fractional expressions Patterns, rela..