if are two positive numbers whose sum is 30

From the two examples it is seen that the signs of the terms of a GP must either be all alike or alternatively positive and negative. Note that the numbers in continued proportion are in GP, i.e.,..

>If A, G, H are the A.M., G.M., H.M. respectively between non-zero positive numbers a and b, then (a) A, G, H are in G.P. (b) A>G>H. In particular, if a = b = c, then A = G = H. (i) A sequence is said to be an arithmeticco-geometric sequence if terms of the sequence are th..

If Z 1 = a + ib and Z 2 = x + iy, then we define their sum as Z 1 + Z 2 = (a + ib) + (x + iy) = (a + x) + i(b + y) which is a complex number..

Working rules for finding the greatest term: Step 1: In (a + b) n , the constants a and b must be positive. Step 2: Write T r+1 and T r and find the value of T r+1 /T r . Step 3: Simplify the inequality (T r+1 /T r ) greater than or equal to 1 an..

Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method). We have, (a + b) n = (a + b) (a + b) ....... n times. The terms on the RHS are obtained by taking one letter from each factor and multiplying them together. Choosing 'a' from all the factors, ..

Consider the GP a, ar, ar 2 ... ..

If a and b are positive numbers, then the above method can also be applied to find the numerically greatest term in the expansion of (a - b) n..

Find all pairs of factors whose product is the last term of the trinomial. From the pairs of factors from step 1, choose a pair of factors whose sum is the coefficient of the middle term of the trinomial. Split the middle term using the pair of factors from step 2 a..

1. Find the sum to the series 1+2x+3x 2 +.... to n terms and to infinity when x < ..

Square root of a negative number is known as an imaginary number . If x and y are real numbers, then x + iy is called a complex number . x is called the real part and y is called the imaginary part . The following are the types of compl..