Question

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

Answer 1

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