Differential calculus

Ques1) Let
f _p (@ ) = (cos@/p² + i sin @ / p²). (cos 2@ / p² + i sin 2@ / p² )...................................(cos@ /p + i sin @/p).

Then lim _{nâ†’âˆž}[|f_n(2 âˆ© )|] is equlas to , where [.] denotes greatest integral function.
(a)-1 (b)1 (c) i (d) - i

2 Answers

f_p(\alpha)=e^{\alpha /p^2}\times e^{2\alpha /p^2}\times e^{3\alpha /p^2}\times .... \times e^{p\alpha /p^2}

f_p(\alpha)=e^{\alpha /p^2+2\alpha /p^2+3\alpha /p^2+...+p\alpha /p^2}

f_p(\alpha)=e^{(1+2....p)\alpha /p^2}=e^{p(p+1)\alpha /2p^2}=e^{(p+1)\alpha /2p}

Now can you finish this one?

Yups
thanx a lot sir

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