Chứng minh rằng S= 5+ 5^2 + 5^3 + ...+ 5^1991 + 5 ^1992 chia hết cho 6

Mathematics

1 answer:

marin [14]2 years ago

3 0

Answer:

steps below

Step-by-step explanation:

5¹+5² = 30 30/6 = 5¹

5³+5⁴ = 125 + 625 = 750 750/6 = 125 = 5³

5⁵+5⁶ = 18750 18750/6 = 3125 = 5⁵

...........

(5¹⁹⁹¹+5¹⁹⁹²)/6 = 5¹⁹⁹¹

sum of every couple consecutive multiple of 5 are multiple of 6, the sum

S= 5+ 5^2 + 5^3 + ...+ 5^1991 + 5 ^1992 IS multiple of 6

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