Question

Tính tổng

A =1+6+6²+6⁴+...+6¹⁰⁰

B =1+3²+3⁴+3⁶+3⁸+...+3¹⁰⁰

C =1+3³+3⁶+3⁹+3¹²+...+3¹²⁰

Answer 1

\(A=1+6+6^2+6^4+...+6^{100}\)

\(\Rightarrow6A=6+6^2+6^4+...+6^{100}+6^{101}\)

\(\Rightarrow6A-A=\left(6+6^2+6^4+....+6^{102}\right)-\left(1+6+6^2+6^4+...+6^{100}\right)\)

\(\Rightarrow5A=6^{101}-1\)

\(\Rightarrow A=\frac{6^{101}-1}{5}\)

Answer 2

\(B=1+3^2+3^4+3^6+3^8+...+3^{100}.\)

\(\Rightarrow3B=3^2+3^4+3^6+...+3^{101}\)

\(\Rightarrow3B-B=\left(3^2+3^4+...+3^{101}\right)-\left(1+3^2+3^4+...+3^{100}\right)\)

\(\Rightarrow2B=3^{101}-1\)

\(\Rightarrow B=\frac{3^{101}-1}{2}\)