Question

Determinați ultima cifră a numerelor:
A) b=7+7 la puterea 2+7 la puterea 3+...+7 la puterea 43;
B) c=3 la puterea 0+3 la puterea 1+3 la puterea 2+ 3 la puterea 3+...+3 la puterea 42;
C) d=8+8 la puterea 2+8 la puterea 3+...+8 la puterea 88.
Help, please!Thanks!!

Answer 1

b=7(1+7+7² +...+7^42) =7[(1+7+49+343) +7^4·(1+7+49+343).. + 7^39 ·(1+7+49+343)] b = 7·400(1+7^4+ .......+ 7^39)⇒ Ucifra(b) = 0
c = 1+ 3+3² + 3³ +......+3^42 = (1+3 +9 + 27) + 3^4 ·(1+3+9+27)+....+3^39(1+3+9+27)
c = 40(1+ 3^4 +..........+ 3^39 ) ⇒ Uc(c) = 0
d = (8 + 64 +512 +4096) +8^4 ·(8 + 64+512+4096) +.......+8^84·(8+64+512+4096)
d = 4680(1+ 8^4 +........+ 8^84) ⇒Uc(d) = 0