number theory pi

i) The series formed by the reciprocals of the terms of a geometric series is also a geometric series. ii) There is no general method of finding the sum of a harmonic progressi..

Let n N and P(n) denote a certain statement or formula or theorem. Then P(n) holds good for every natural number n if (i) it holds for n = 1 and (ii) it holds for n = k+1 whenever it holds for n =..

i) 1 + 4 + 7 + 10 + ... is a series in which first term is 1, second term is 4, third term is 7 and so on. ii) 3 - 9 + 27 - 81 + ... is also a series in which the first term is 3, second term is -9, third term is 27 and so ..

Irrational Numbers - Numbers which are not rational are called irrational numbers. When expressed as decimals, they are non-terminating and non-recurring. i.e., Irrational numbers cannot be put in the form where and are some examples of irrationals. (i) ..

(i) P(1) is true (ii) P(r) is true P(r+1) is tr..

can be represented on the number line. (i) For every real number, there is a corresponding point on the number line. (ii) For every point on the number line, there exists a real number. Express with rational denominator. Expre..

Absolute Error and Percentage Relative Error - From the above examples on approximation, we observe that the approximated value may be more or less than the original number. The difference between these two values is called the absolute error. Absolute Error = Original number - ..

i) (1 + 2x) - 4 ..

Let us consider the marks obtained by four students in Physics, Chemistry and Biology for the first unit test. We have represented the data in rows and columns. (i) Rows show the marks obtained by each student. (ii) The columns show the marks in Physics, Chemistry, Biology obtained by each stu..

Introduction - Let us consider the marks obtained by four students in Physics, Chemistry and Biology for the first unit test. We have represented the data in rows and columns. (i) Rows show the marks obtained by each student. (ii) The columns show the marks in Physics, Chemistry, Biology obtai..