sum of positive numbers

>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..

Some particular expansions for Positive Integral Index - For n N, we have: a) (a - b) n (a +(- b))..

The number of terms in the expansion of (a + b) n depends on the index n. The index n is either even or o..

Particular Terms for Positive Integral Index - Sometimes, a particular term satisfying certain conditions is required in the binomial expansion of the type (a + b) n . This can be done by expanding (a + b) n and then locating the required term. Generally this becomes a tedious task, speci..

The number of terms in the expansion of (a + b) n depends on the index n. The index n is either even or od..

In (a + b) n , let 'a' and 'b' be both positive numbers. As r increases, the factor decreases. So long as this factor is greater than 1, T r+1 remains greater tha..

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 , decreases the po..

For n N, we have: a) (a - b) n (a +(- b))..

Sometimes, a particular term satisfying certain conditions is required in the binomial expansion of the type (a + b) n . This can be done by expanding (a + b) n and then locating the required term. Generally this becomes a tedious task, specially when the index n is large. In such cases, we begin b..

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 , ..... n C n ..