Home/ Intrebari/Q 64249
Urmator
In Process

AniDeȘcoală.ro Latest Intrebari

dragosh96dn
Pe: 2007-10-31T16:21:58+02:00 In: In:

problema d cls a 5a!!!va rog dak putetzi sa imi raspundetzi!

Aflatzi ultima cifra a numarului:
n=1+3*5*7+3*5*7*9+5*7*9*11+……………….+95*97*99*101 🙄 ❓ 🙁 :mrgreen:

Similare

4 raspunsuri

  1. mateclub

    formulare neclara, scuza-ma nu pot sa te ajut.

  2. racketa
    veteran (III)

    Fiecare termen dintre 3*5*7, 5*7*9, etc are ultima cifra egala cu 5. Mai ramane sa gasim numarul acestor termeni.
    Ultimele numere in fiecare termen sunt 7, 11, …. 101 deci anteriorul plus 2. Avem 101=7+2*47 si rezulta 48 termeni.
    Ultima cifra este deci 1+5*48 => 1+0=1

  4. racketa
    veteran (III)

    m-am uitat putin mai bine la termeni si nu prea e clar cum se obtin. M-am grabit solutia mai devreme…
    Scuze !

  5. dan
    expert (VI)

    dragosh96dn wrote: Aflatzi ultima cifra a numarului: n=1+3*5*7+3*5*7*9+5*7*9*11+……………….+95*97*99*101 🙄 ❓ 🙁 :mrgreen:

    n=1+1*3*5*7+3*5*7*9+5*7*9*11+……………….+95*97*99*101
    \underbrace{1*3*5*7;\;3*5*7*9;\;5*7*9*11;\;7*9*11*13;\;9*11*13*15\;}_{=5\;termeni}\\ \underbrace{11*13*15*17;\;..................................................;\;19*21*23*25}_{=5\;termeni}\\ .....................................................................................................................\\ \underbrace{81*83*85*87;\;..................................................;\;89*91*93*95}_{=5\;termeni}\\ \underbrace{91*93*95*97;\;93*95*97*99;\;95*97*99*101;}_{=3\;termeni}\\ Avem \;deci\; U_c\({\underbrace{9\cdot(5\;termeni)}_{U_c=5}+\underbrace{3\;termeni}_{U_c=5}+1}\)=1

Raspunde

Raspunde