log sum inequality

Introduction Exponential and Logarithmic Series - 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 coeff..

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 real number such that |x|<1, ..

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 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 a sum and we denote ..

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 ..

Of all the straight lines that can be drawn to a given straight line from a point outside it, the perpendicular is the shortest. P is a point outside the straight line AB. PM is perpendicular to AB. PQ is any other line from P to AB. PM < PQ In a right angled triangle, the hypotenuse is the grea..

The sum of two consecutive even numbers is less than 70. Choose an equation or inequality to find the maximum possible values of the numbers. => 2 n + 1 = 70 or n + n + 2 > 70 or 2 n - 2 ≤ 70 or n + n + 2 < 70..

Write and solve the inequality obtained from the statement: "The sum of a number x and 5 is greater than or equal to 8." => x ≤ 3 or x > 3 or x < 3 or x ≥ 3..

21 years ago, Francis was thrice as old as Sunny. The sum of their present ages is 90. Choose an equation or an inequality to find their present ages. Let c represent present age of Francis in years. => c - 21 = 3 (90 - c - 21) or c - 21 = 90 or c + 90 = 21 or c - 21 = c - 90..

Express the inequality 25 x > 120, as a word sentence. Let x represent the number. => The sum of 25 and a number is greater than 120 or The product of 25 and a number is less than 120 or The product of 25 and a number is greater than 120 or The sum of 25 and a numbe..