Question

A₁=1+2+3+...+167

A₅=4³+4⁴+4^5+...+4¹⁰⁰

Answer 1

\(A_1=1+2+3+...+167\)

\(A_1=\left(167+1\right).167:2\)

\(A_1=168.167:2\)

\(A_1=28056:2\)

\(A_1=14028\)

 

\(A_5=4^3+4^4+4^5+...+4^{100}\)

\(4\text{A}_5=4^4+4^5+4^6+...+4^{101}\)

\(4\text{A}_5-A_5=\left(4^4+4^5+4^6+...+4^{101}\right)-\left(4^3+4^4+4^5+...+4^{100}\right)\)

\(A_5=4^{101}-4^3\)

Answer 2

A=1+2+3+...+167

A có: (167-1)+1=167(số hạng)

A=(167+1)*167/2=14028

B=4³+4⁴+4⁵+...+4¹⁰⁰

4B=4⁴+4⁵+4⁶+...+4¹⁰¹

4B+4³=4³+4⁴+4⁵+...+4¹⁰⁰+4¹⁰¹=B+4¹⁰¹

4B-B=4¹⁰¹-4³

3B=4¹⁰¹-4³

B=(4¹⁰¹-4³)/3