Question

determinati ultima cifra a numerelor
$determinati \: ultima \: cifra \: a \: numerelor \\ \: c = {3}^{0} + {3}^{1} + {3}^{2} + {3}^{3} + ... + {3}^{42}$
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Answer 1

Explicație pas cu pas:

c=3⁰+3¹+3²+...+3⁴²/×3

3c=3¹+3²+3³+....+3⁴²+3⁴³

Le scadem si avem:

3c-c=3¹+3²+..+3⁴³-3⁰-3¹-3²-...-3⁴² =>

=>2c=3⁴³-3⁰ =>

2c=3⁴³-1

U.C 3⁴³=7 => u.c 2c=6 => u.c c=3