if are two positive numbers whose sum is 60

Hence h 1 , h 2 ,....h n are the n harmonic means. If A, G and H respectively are arithmetic, geometric and harmonic means of two positive quantities a and b, then G 2 = A.H and A ≥ G ≥..

>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..

An irrational root of a positive rational number is called a surd. Consider a number with base 'a' as a positive rational number with power of a fraction, say then Since is an n t h root, it is called a surd of order n, if it is irrational...

General Term for Positive Integral Index - For n N, we have . Let T r + 1 (0 r n) be the (r+1) t h term in the expansio..

Working rules for expanding (a + b) n n N: Step 1: The value of index, n implies that there will be n+1 terms in the expansion of (a + b) n . Step 2: Write the first term: n C 0 a n b 0 . Step 3: For the second term, take coefficient as n C 1 , decrea..

n C 0 , n C 1 , ..... n C n are called binomial coefficients. n C 0 , n C 2 n C 4 , ..... are called even binomial coefficients. n C 1 , n C 3 , n C 5 .... are called odd binomial coefficients. In case of no ambiguity, the binomial coefficients n C 0 , n C 1 , .....

Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..

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..

1. To find the sum of first n natural numbers. 2. To find the sum to squares of first n natural numbers. 3. To find the sum to the cubes of first n natural numbers. 4. Method of finding sum of a ser..

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..