evaluate limx-2 ((1+x)^n-1)/x
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For Limit x-2 it is very simple put x=2 in function and get answer
But in your question limit may be x-0
limx-0 [(1+x)^n-1]/x
using binomial expansion
=limx-0 [(nC₀ x⁰+ nC₁ x¹+nC₂ x²+.....+nCnx^n)-1]/x
=limx-0 [1+nx+ nC₂x+........m +nCn x^n -1 ]/x
=limx-0 x[n+nC₂x+....+nCn x^(n-1)]/x
=limx-0 [n+nC₂x+.......+ nCn x^(n-1)]
=limx-0 [n+0+....+0]
=n
But in your question limit may be x-0
limx-0 [(1+x)^n-1]/x
using binomial expansion
=limx-0 [(nC₀ x⁰+ nC₁ x¹+nC₂ x²+.....+nCnx^n)-1]/x
=limx-0 [1+nx+ nC₂x+........m +nCn x^n -1 ]/x
=limx-0 x[n+nC₂x+....+nCn x^(n-1)]/x
=limx-0 [n+nC₂x+.......+ nCn x^(n-1)]
=limx-0 [n+0+....+0]
=n
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