24hint::
No of distinct terms in multinomail expansion
(x1+x2+x3+..+xn)r=n+r-1Cr
If n is an even integer and a,b,c are distinct numbers,then find the number of distinct terms in the expansion of
(a+b+c)^n + (a+b-c)^n
My approach>>>>
It should b (n+1)+(n-1)+(n-3)+........+1
So ans should b ((n+2)/2)
But ans given is [((n+2)^2)/2]
Please help..
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14 Answers
24
1I used dat eureka to get the final result..It should b r-1 instead of r in ur formula..I reached this conclusion using dis only..
62Hint: Find number of terms in (a+b-c)n where power of c is even
Do you see why i have given this hint?
1Yes bhaiya i can..As tems even of (a+b+c)^n and (a+b-c)^n cancels out
If we suppose a+b as x..
Nd then expand according to binomial theorem fr positive integers..
M i correct??
Bt after solving i m nt getting d ans..
62yes.. you can do that too..
so find the terms with even powers of c and for each such power, count the number of those terms in the expansion of (a+b)^k
1Then it comes out to b..
(n+1)+(n-1)+(n-3)+........+1
And this adds upto
((n+2)/2)
Bt its incorrect according to the answer given in the book..
1Anyone please solve it and confirm my answer please..Thanks nishant bhaiya and eureka fr u genuine try..Thanks a lot))
341why dont you check whether u have added correctly? u can see u have made a mistake because the sum of terms in AP is coming out to be a linear polynomial instead of a quadratic.
1Yeah prophet i got it..Thanks alot dude..Answer given in the book is wrong...