Câu hỏi của Nguyễn Gia Bảo

Question

Tính tổng

A =1+6+6²+6⁴+...+6¹⁰⁰

B =1+3²+3⁴+3⁶+3⁸+...+3¹⁰⁰

C =1+3³+3⁶+...

❤ Hoa ❤ · Accepted Answer

$A=1+6+6^2+6^4+...+6^{100}$

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

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

$\Rightarrow5A=6^{101}-1$

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

Câu trả lời:

$A=1+6+6^2+6^4+...+6^{100}$

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

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

$\Rightarrow5A=6^{101}-1$

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

❤ Hoa ❤ · Answer

$B=1+3^2+3^4+3^6+3^8+...+3^{100}.$

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

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