Question

aflati ultimele doua cifre ale sumei s=1+2*3+3*4*5+6*7*8*9+....+36*37*38*....*44

Answer 1

1 + 2*3 +3*4*5 + 6*7*8*9 +  10*11*12*13*14 + 15*16*17*18*19*20 + 21*22*23*24*25*26*27 + 28*29*30*31*32*33*34*35 + 36*37*38*39*40*41*42*43*44
are ultimele cifre in modul urmator:


-2*3=6
-3*4*5=60
-6*7*8*9=3024
-10*11*12*13*14 =>40 pt. ca 4*2*3=24 cu 0 in coada de la 10
-15*16*17*18*19*20 are ultimele 2 cifre 00 pt. ca 15*16 are ultima cifra 0,+inca un 0 de la 20
-21*22*23*24*25*26*27 are ultimele 2 cifre 00 pt. ca 25=5*5 inmultit cu 24=2*2*6 inseamna 25*24=5*5*2*2*6=10*10*6
-28*29*30*31*32*33*34*35 are ultimele 2 cifre 00 pt. ca 35*36 are ultima cifra 0,+inca un 0 de la 30
-36*37*38*39*40*41*42*43*44 are asa: 6*7*8*9=3024, 2*3*4=24, deci 24*24=576 , 76*40=3040

⇒
 1+6+ 60+24+40+00+00+00+40=7+100+24+40=171