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"t >,nt -12 +22 +32+...+ ,r? :u('+1\2'1+1)A'= I

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t+(t+z)+(r +z+:)*...+(1+ 2+3+...+n)=' l ""r " " r'a rl

z +(z+ a)+ Q + q+ 6)+. .. +(2+ 4 + 6 +... +2n) :r + (r +:)*(i+l +s)+... + (r+ 3 +5 +... + (2r-'1)) =

tt *tt +zz)+(tt +z= +st)+...*(it +22 +32 +...+ ,=)=

zt *b'++')+Q'+42 +q')* ...:b'+42 +62+...+(z"f )=tr +(t2 +:2)+(i' *t' +s2)+...*h' +32 +52 +...+(1-r)t)=tt *(tt +f)+(l'*z-'+r3)+-.-*(i' +23 +33 +"-.+rr3)-

zt *(zt*+i)*(z'+43 +ot)* ..*(zt +43 +63 +...+(2,,f ):r'' +(r3 +r')+(tt *st +s3)+...*ht +33 +53 +...+ (zr-r)t)=I . 2 i (t. z + z. t)* (t . z * i. 3 + 3 . +)+... + (l . 2 + 2. 3 + 3' 4 +... + r,(,r + l)) :.

,dpor#o-{za ltt ' kfq^/t prof yr;:nr,rro

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25.

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-6-

Partea intreaga si partea fi'actionala

Defi [rJ: -u-r ltt. Zip < ti€ Cel mai mare intreg mai mic sau eEal cu x

Def, !r]:'-lx]r Partea h'actionara {zecimalat

Proorietati:Il-

;a-

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6,

8.

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Vn e &'*

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t

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9"

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11.

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* L,-l

[*l* [- r]=f---' o',l+- I1_.

{'}* {- x} *--* o5j--l It!

{11

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pr* ["

.;]- ['

. ;] : r:'l

r.r f Il I zl l- n'1[-rJ+l,r*- l+l "

* - I+.. +i,r+-1 | = f".r1L nJ L n) | n i

12. [xi+ ["]= h + r,1. Lri+ Ivl+ rig]* [a]* t l. f" *i * ritt"i+ fal+ lc7+ z

u k-1.[r;,-li-:i L r=l J

e Cu cat este mai mare memb.rl dreot decat cel stanq?u Cand are loc egalitatea?

i 3. Fie r e iv- * si p nurnar prim- Cel rnai mare numar numar natural k--lr-tT-l

pentru care p'lrri este k :l ' l. | + l. I i l*. *l lJ Lp'i Lp'l

. | "/,I i. .,,,Vn e N *'i li- l'r'r,, i i"{

Modulul i , ,--"1; ;. "

Dei:

Proprietati:i. i'i. o

daca x>0ciaca x:0daca x<0

v-reR

f-, r l*i-xl: J u

1

2. iti:0 4a v: f;

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5" lxi<c( e-s1x1ctIti.oe-s<x<cr

a>0a*0

6. i'*yislri+iri. Se verifica prtn egalitate daca x si y au aceiasi semnr Se verifica prin < daca x si y au semen confrare

l+a+b+ci<iai+iai+[4la, + a1 + a3 +...* o,i

= i", i +ia,,i+iori *"". +io,l

i-n- i n ;r"f:'l: :' ,*i 11.,,,/!:i-: :.4,': *iI".l<Ilo,llu /-ft ^li k=r I t:l

. Mociuiui sumei este mai mic sau eeai decat suma moduleiorI!{

€ Se verifica prin egai daca'2 numere sunt de acelasi sefiln. Se verifica prin < daca cele ? numere au sefilne contrare

i- ri = 1xi-->2 numere opuse au acelasi modul

7 . ii'i- i/ii si* - yi

iti = maiii-",ri (Definitie echivaienta)

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= v

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Mate 9

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Transcript of Mate 9