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Case 2: n is odd.
Let n = 2k+1 The number of terms is n+1 i.e., (2k + 1) + 1 = 2k + 2. In this case, there are two middle terms and are after k terms. Thus, in (a + b) n : ..
Let n = 2k+1 The number of terms is n+1 i.e., (2k + 1) + 1 = 2k + 2. In this case, there are two middle terms and are after k terms. Thus, in (a + b) n : ..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..
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 insert n Harmonic Means between two given quantities
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 b. Let d = common difference of the A.P. ..
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 b. Let d = common difference of the A.P. ..2nd Method:
from 1 s t method Let x = 24 k and y = 5k (i) (ii) Ans: (i) , (ii..
from 1 s t method Let x = 24 k and y = 5k (i) (ii) Ans: (i) , (ii..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...
Step 2:
Assume the validity of the result for n equal to some arbitrary but fixed natural number, say, ..
Note 2:
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 coeffic..
Step 2:
The first term in (1 + x) n is always ..
Step 2:
Find the general terms T r + 1 in the expansion of (1+x) n..
Result
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