Question

RÚT GỌN

B = 3 + 3^2 + 3^3 + 3^4 + ... + 3^50

C = 4 + 4^2 + 4^3 + 4^4 + ...+ 4^2018

Answer 1

\(B=3+3^2+3^3+3^4+...+3^{50}\)

\(\Rightarrow3B=3^2+3^3+3^4+3^5+...+3^{51}\)

\(\Rightarrow2B=3^{51}-3\)

\(\Rightarrow B=\frac{3^{51}-3}{2}\)

\(C=4+4^2+4^3+4^4+...+4^{2018}\)

\(\Rightarrow4C=4^2+4^3+4^4+4^5+...+4^{2019}\)

\(\Rightarrow3C=4^{2019}-4\)

\(\Rightarrow C=\frac{4^{2019}-4}{3}\)

Answer 2

\(B=3+3^2+3^3+...+3^{50}\)

\(\Rightarrow3B=3^2+3^3+3^4+....+3^{51}\)

\(\Rightarrow3B-B=\left(3^2+3^3+3^4+...+3^{51}\right)-\left(3+3^2+...+3^{50}\right)\)

\(\Rightarrow2B=3^{51}-3\)

\(\Rightarrow B=\frac{3^{51}-3}{2}\)

\(C=4+4^2+4^3+...+4^{2018}\)

\(\Rightarrow4C=4^2+4^3+4^4+....+4^{2019}\)

\(\Rightarrow4C-C=\left(4^2+4^3+4^4+...+4^{2019}\right)-\left(4+4^2+4^3+...+4^{2018}\right)\)

\(\Rightarrow3C=4^{2019}-4\)

\(\Rightarrow C=\frac{4^{2019}-4}{3}\)

Answer 3

         \(B=3+3^2+...+3^{50}.\)

\(\Leftrightarrow3B=3^2+3^3+....+3^{51}\)

\(\Leftrightarrow3B-B=3^2+3^3....+3^{51}-\left(3+3^2+3^3+...+3^{50}\right)\)

\(\Leftrightarrow2B=3^{51}-3\)

\(\Leftrightarrow B=\frac{3^{51}-3}{2}\)

       \(C=4+4^2+....+4^{2018}\)

\(\Leftrightarrow4C=4^2+4^3+....+4^{2019}\)

\(\Leftrightarrow4C-C=4^2+4^3+...+4^{2019}-\left(4+4^2+....+4^{2018}\right)\)

\(\Leftrightarrow3C=4^{2019}-4\)

\(\Leftrightarrow C=\frac{4^{2019}-4}{3}\)

Answer 4

HT nha bạn