Sunday, 12 May 2019

calculus - Show that the sequence sqrt2,sqrt2+sqrt2,sqrt2+sqrt2+sqrt2+... converges and find its limit.

Setting an=2+2+2+  I get that an+1=2+ana1=2. Clearly all numbers in the sequence are positive and we see that $a_n


We can use the help-function f(x)=2+x such that an+1=f(an). But since f(x)=122+x=0no real solutions,



f(x) never flattens out or decreases, so it can't be convergent?

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real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...