Bai 1: Tinh

a) ( \(\frac{1}{3}\))^-1 - (\(\frac{-6}{7}\))⁰ + ( \(\frac{1}{2}\))^{-2 .} 2

b) \(\frac{2.5^{22}-9.5^{21}}{25^{10}}\): \(\frac{5.\left(3.7^{15}-19.7^{14}\right)}{7^{16}+3.7^{15}}\)

c) ( \(\frac{-4}{9}\))³. (\(\frac{3}{2}\))². (\(\frac{9}{6}\))³

A =5+ 5²+5³+..................................................+5¹⁰⁰

B= 5+5³ +5⁵ +...................................................+5⁹⁹

C= 1+ \(\frac{1}{3}\) + \(\frac{1}{3^2}\) +....................................+ \(\frac{1}{3^{100}}\)

D= 1-\(\frac{1}{3}\)+ \(\frac{1}{3^2}\) - ..........................................- \(\frac{1}{3^{99}}\)+\(\frac{1}{3^{100}}\)

E=\(\frac{1}{2}\)+\(\frac{2}{2^2}\)+\(\frac{3}{2^3}\) +................................... +\(\frac{100}{2^{100}}\)

D= \(\frac{x^2-2x+2000}{x^2}\)= 1-\(\frac{2x}{x^2}\)+\(\frac{2000}{x^2}\)

Đặt t= \(\frac{1}{2}\)=> D= 2000t²-2t+1 = (\(20\sqrt{5}t\))²-2.\(20\sqrt{5}t\).\(\frac{1}{20\sqrt{5}}\)+\(\left(\frac{1}{20\sqrt{5}}\right)^2\)\(-\left(\frac{1}{20\sqrt{5}}\right)^2\)+1

D= (\(20\sqrt{5}t\)-\(\frac{1}{20\sqrt{5}}\)) ²+\(\frac{1999}{2000}\)\(\ge\)\(\frac{1999}{2000}\)

Min D= \(\frac{1999}{2000}\)khi \(20\sqrt{5}t\)\(-\frac{1}{20\sqrt{5}}\)= 0 => t = \(\frac{1}{2000}\)=> \(\frac{1}{x}\)= \(\frac{1}{2000}\)=> x= 2000

Tìm x, y, z phù hợp với quy tắc với các câu đố.

A) 0 ➜ 1 ➜ 1 ➜ 2 ➜ 3 ➜ 5 ➜ 8 ➜ 13 ➜ x ➜ 34 ➜ 55.

B) (a + b) ➜ (ba + cb) ➜ (bca + byd) ➜ (cdab + edbc).

C) Viet = 56 ; Nam = 28 ; Meow = 56 ➜ (z – y)² = ... Vậy: S = 2,775k² – x² – 2y² – z² là

1, Rút Gọn Biểu Thức :

A = \(2:\frac{5}{2}-19\frac{2017}{2018}:\frac{12}{5}+17\frac{2017}{2018}:\frac{12}{5}\)

5, Cho S = \(1+5\)+\(5^2+5^3+5^4+...+5^{2014}\)

a) Tính tổng S

b) Tìm số dư của  \(5^{2015}\)khi chia 4.

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