Question

A= 1 + 3¹+ 3² + 3³ + 3⁴ + ... + 3¹⁰⁰ - 3¹⁰¹: 2 + 5

Mọi người giải nhanh giúp mình nha, mình cần gấp.

 

Answer 1

\(A=1+3+3^2+3^3+3^4+...+3^{100}-3^{101}\div2+5\)

\(3A=3+1+3+3^2+3^3+...+3^{100}\div2+5\)

\(3A-A=\left(1+3+3^2+3^3+3^4+...+3^{100}+3^{101}\right)-\left(3+1+3+3^2+3^3+...+3^{100}\right)\div2+5\)

\(2A=1+3+3^2+3^3+3^4+...+3^{100}+3^{101}-3-1-3-3^2-3^3-...-3^{100}\div2+5\)

\(2A=3-3^{101}\div2+5\)

\(2A=3-3^{101}\div2^{101}+5\)

\(2A=3-1+5\)

\(2A=7\)

\(\Rightarrow A=14\)