Algebra

  • Formulas and Results of Permutations Combinations and Binomial Theorem

    1. Factorial of is defined as , where is natural number. 2. (Permutation) 3. (Combination) 4. 5. 6. 7. 8. For large , is called Striling Approximation Formula. 9. 10. , , , 11. , 12. If is positive integer, then 13. 14. General Term 15. If is not positive integer, then the binomial expansion […]

  • Formulas of Sequence and Series

    The term of the Arithmetic Progression (A.P) is given by .   Arithmetic mean between and is given by .   If denotes the sum up to terms of A.P. then where stands for last term,   The sum of A.M’s between and is .   The term of the geometric progression is .   […]

  • Results and Formulas of Equations

    If and are the roots of the Quadratic Equation , then Sum and products of the roots and of is given by and is called Discriminant of The roots of the quadratic are imaginary if is negative. real if is positive or zero. real and equal if real and rational if and is a perfect […]

  • Logarithm Formulas

    1.   if and only if , and , is positive number. 2.   3.  , , i.e. 4.   5.   6.   7.   8.   9.   10. 11. 12.

  • Exponents Formulas

    1. If is positive integer, and , then to factors. 2. ,        , 3. ,         ; 4. 5.          ; 6.         7. ,        ; 8.         ; 9.         ; 10.         ;

  • Ratio and Proportion Formulas

    1. If then 2. If then 3. If then 4. If then 5. If then 6. If then called Componendo-Dividendo Rule. 7. If then 8. If and then 9. If and then 10.  If then 11.  If then 12.  If  then 13.  If 14.  If then 15.  If then 16.  If then