Question

1. So sánh:

a. 1 và \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.....+\frac{1}{2^{50}}\)

b. \(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+.....+\frac{1}{3^{100}}\)với \(\frac{1}{2}\)

c. \(\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^6}+.....\frac{1}{4^{1000}}\)với \(\frac{1}{3}\)

2. Tìm x, biết:

a.\(\left(\frac{2}{5}-x\right):1\frac{1}{3}+\frac{1}{2}=-4\)

b.\(3-\frac{1-\frac{1}{2}}{1+\frac{1}{x}}=2\frac{2}{3}\)

c.\(4^x+4^{x+3}=4160\)

d.\(2^{x-1}+5.2^{x-2}=\frac{7}{32}\)

e.\(\frac{x-100}{24}+\frac{x-98}{26}+\frac{x-96}{24}=3\)

g.\(\frac{x-1}{65}+\frac{x-3}{63}+=\frac{x-5}{61}+\frac{x-7}{59}\)