Question

a,Tính tổng:S=1+5²+5⁴+...+5²⁰⁰

b,So sánh 2³⁰+3³⁰+4³⁰ và 3.24¹⁰

Answer 1

a) S=1+5²+5⁴+.....+5²⁰⁰

=>5²S=25S=5²+5⁴+5⁶+.....+5²⁰²

=>25S-S=(5²+5⁴+5⁶+....+5²⁰²)-(1+5²+5⁴+......+5²⁰⁰)

=>24S=5²⁰²-1

=>S=\(\frac{5^{202}-1}{24}\)

Answer 2

a) lấy 5S-S

b)trên olm có

Answer 3

b) Ta có: \(4^{30}=2^{30}.2^{30}=\left(2^3\right)^{10}.\left(2^2\right)^{15}=8^{10}.4^{15}>8^{10}.3^{15}>8^{10}.3^{11}=8^{10}.3^{10}.3=3.24^{10}\)

Vậy \(2^{30}+3^{30}+4^{30}>3.24^{10}\)

Answer 4

b) Link nè

https://hoc24.vn/hoi-dap/question/393164.html