Question

Cum aplic criteriul clestelui pt a afla limita sirului $a_{n}$ = $\frac{sin n}{2^{n} }$

Answer 1

-1≤sinn≤1 |*1/2ⁿ<=>-1/2ⁿ≤an≤1/2ⁿ

lim-1/2ⁿ=-1/+∞=0

lim1/2ⁿ=1/+∞=0

lim-1/2ⁿ=lim1/2ⁿ=>(C.C.):∃lim(an)=lim(sinn/2ⁿ)=0