Question

Bài 1 :Tính tổng

a, C=5¹⁰⁰+5¹⁰¹+..............................+5¹⁵⁰

b,choD=1+6+6²+.............................+6²⁰

Chứng minh rằng : 5D+1 luôn chia hết  cho 6

Answer 1

\(C=5^{100}+5^{101}+....+5^{150}\)

\(5C=5^{101}+5^{102}+...+5^{151}\)

\(4C=5^{151}-5^{100}\)

\(C=\frac{5^{151}-5^{100}}{4}\)

Answer 2

\(D=1+6+6^2+...+6^{20}\)

\(\Rightarrow6D=6+6^2+6^3+....+6^{21}\)

\(\Rightarrow5D=6^{21}-1\)

\(\Rightarrow5D+1=6^{21}\)

Vì \(6^{21}⋮6\) nên \(5D+1⋮6\)