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solve the equation
1 - x + x(x-1)/1.2 - x(x-1)(x-2)/1.2.3 + ...... +(-1)nx(x-1)(x-2)....(x-n+1)/n! = 0
putting x=n in the equation, it becomes
nC0-nC1+nC2.........+ (-1)n nCn = 0
so x=n is a solution.
how can we say that no other solution exists.
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8 Answers
1IF
1 - x + x(x-1)/1.2 - x(x-1)(x-2)/1.2.3 + ...... +(-1)nx(x-1)(x-2)....(x-n+1)/n! = 0
as you have not mentioned the equality...
then
x=1
is another solution !
1i have already told that x=n is a soln.
also x=1,2,3,....... n
i want to whether non-integral solutions exist.
and if they dont exist how to prove that they dont.
62see this is a polynomial of nth degree..
so it cant have more than n roots
you know n roots already :)