Question

Tìm số tự nhiên n biết:

\(\frac{1}{9}.27^n=3^n\)

\(3^{-2}.3^4.3^n=3^7\)

\(2^{-1}.2^n+4.2^n=9.2^5\)

\(32^{-n}.16^n=2048\)

Tìm x thuộc Z biết:

\(2^{x+2}-2^x=96\)

\(7^{x+2}+2.7^{x-1}=345\)

\(3^{x-1}+5.3^{x-1}=162\)

Answer 1

\(A=1+3+3^2+3^3+...+3^{101}\)

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

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

\(2A=3^{101}-1\)

\(A=\left(3^{101}-1\right):2\)

Answer 2

Thu gọn tổng sau:

A=1+3+3²+3³+...+3¹⁰⁰ 

B= 2¹⁰⁰-2⁹⁹-2⁹⁸-2⁹⁷-...-2²-2

C= 3¹⁰⁰-3⁹⁹+3⁹⁸-3⁹⁷-...+3²-3+1