IIT JEE , AIEEE Forum - Mathematics , Algebra

sanjay_me

how to find a largest term in a expansion when the value of x is specified?

anybody plz answer this

nano0101

well i dont know soo well nut here is my try at this

If (x+a)ⁿis the expression we can expand it thru binomial theorem there are three possibilities:

if x>a:
then
ⁿC₀xⁿwill be the highest

if x=a:
ⁿC_n/2x^n/2a^n/2 will be the highest

prathima

i think ur approach is wrong
consider this
(1+2)^20
according to u it is 20c20 2^20
but consider the term before it i.e 20c19 2^19 which is greater than the above
i dont know the process actually
but urs is wrong

nano0101

ya the above one works only if n<x>a

prasad_aspirant

u r correct

nano0101

now got it ....
and when n>x>a

the general term is ⁿC_rx^n-ra^_rthe coefficient of all the terms after n=x will be more than xⁿ
Here we are concerned with the coefficient only:
ⁿC_r= n!/[(n-r)!r!]

therefore the largest term will be that term where r satisfies or nearly satisfies the following condition:
(n-r)!r!=x!

do rate me if i am correct

sanjay_me

thank u

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