Question

So sánh:8⁹+7⁹+...+1⁹ và 9¹⁰

Giải nhanh giùm mk với!

Answer 1

Ta có:

8^9+7^9+6^9+5^9+...+2^9+1^9<8^9.8=8^10<9^10

=>8^9+7^9+6^9+5^9+..+2^9+1^9<9^10

CHÚC BẠN HỌC TỐT!

Answer 2

Ta có :

\(9^{10}:9^9=9\)

Và \(\left(8^9+7^9+.....+1^9\right):9^9\)

\(=\left(\dfrac{8}{9}\right)^9+\left(\dfrac{7}{9}\right)^9+..............+\left(\dfrac{1}{9}\right)^9\)

Mà \(\left(\dfrac{8}{9}\right)^9< 1;\left(\dfrac{7}{9}\right)^9< 1;............;\left(\dfrac{1}{9}\right)^9< 1\)

\(\Rightarrow\left(\dfrac{8}{9}\right)^9+\left(\dfrac{7}{9}\right)^9+...........+\left(\dfrac{1}{9}\right)^9< 1+1+1+.....+1=9\)

Vậy \(8^9+7^9+......+1^9< 9^{10}\)