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natima [27]
2 years ago
6

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/<u>6</u> = 5¹

5³+5⁴ = 125 + 625 = 750     750/<u>6</u> = 125 = 5³

5⁵+5⁶ = 18750         18750/6 = 3125 = 5⁵

...........

(5¹⁹⁹¹+5¹⁹⁹²)/<u>6</u> = 5¹⁹⁹¹

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

S= <u>5+ 5^2</u> + 5^3 + ...+ <u>5^1991 + 5 ^1992</u> IS multiple of 6

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