Case 1: n is even.
Let n = 2k The number of terms is n+1 i.e., 2k+1. The middle term has k terms before it. ..
Let n = 2k The number of terms is n+1 i.e., 2k+1. The middle term has k terms before it. ..Expansion of (a+b)^n
Method of writing expansion for (a+b) n - Method of writing expansion for (a+b) n The first term in the expansion of (a + b) n is n C 0 a n b 0 . For the second term, the coefficient is taken as n C 1 , the power of 'a' is decreased by one..
To insert n Harmonic Means between two given quantities
Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and ..
To find the nth term of a GP, whose first term is a common ratio r and number of terms is n
We observe that the index of r on the right hand side is one less than the suffix of t on the left hand side in each of the equalities. Hence t n = ar n - 1 which is the general term of the given G..
We observe that the index of r on the right hand side is one less than the suffix of t on the left hand side in each of the equalities. Hence t n = ar n - 1 which is the general term of the given G..Method of writing expansion for (a+b)n
Method of writing expansion for (a+b) n The first term in the expansion of (a + b) n is n C 0 a n b 0 . For the second term, the coefficient is taken as n C 1 , the power of 'a' is decreased by one and the power of 'b' is increased by one. S..
n Q:..Conclusion
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 =..
Middle Terms for Positive Integral Index
The number of terms in the expansion of (a + b) n depends on the index n. The index n is either even or o..
Step 1:
The value of index, n implies that there will be n+1 terms in the expansion of (a + b) n..
Step I:
Denote the statement involving natural numbers n = 1, 2,. by P(n..
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