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..Example:
If A = {0, 7, 1, 2, 4, 11}, then n (A) = ..
Example:
If A is a set of all positive factors of 36, then in Set builder method it is written as A = {x : x is a factor of 36, x N..
Examples:
(1) " January has 31 days” is a statement. (2) "Null set is a subset of every set” is a statement. (3) "All girls are studious” is not a statement. (4) "Apoorva is honest” is not a statement. Some sentences depend on a variable for its truth value (i..
(1) " January has 31 days” is a statement. (2) "Null set is a subset of every set” is a statement. (3) "All girls are studious” is not a statement. (4) "Apoorva is honest” is not a statement. Some sentences depend on a variable for its truth value (i..Examples :
The following are examples of a finite set. Set of stars in the universe. {x : x N x < 10 10 } {x : x I, x > 0, x is a factor of 156250..
Total number of subsets in a set is 2n
The total number of all possible subsets of a given set containing n elements is 2 n..
To find the nth term of an H.P
To find the n t h term of an H.P, find the n t h term of the corresponding A.P. obtained by the reciprocals of the terms of the given H.P. Now the reciprocal of the n t h term of an A.P. will be the n t h term of the H...
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