Question

Evaluate limit n tends to -1 (1+x+x2±...+x10)

That is x square and x raised to 10

Answer 1

A short proof:

(1+

x

n

)n=enlog(1+

x

n

)

Since log(1+x)=x+O(x2) when x→0, we have nlog(1+

x

n

)=x+O(

x2

n

) when n→+∞