Question

11 Rút​ gọn :

a) A=1+5+5²+5^​3+5⁴+.......+5⁴⁹+5⁵⁰

b) B= \(\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)

Answer 1

a, ta có A.5 = 5 ( 1+5 +5² +...........+5⁴⁹ +5⁵⁰)

5A = 5 +5² +5³ +............... + 5⁵⁰ +5⁵¹

5A-A = (5 +5² +5³ +............+ 5⁵¹) - (1+5+5² +......+5⁵⁰)

4A = 5⁵¹ -1

A =\(\dfrac{5^{51}-1}{4}\)

^{vậy A =}

Answer 2

b, B= \(\dfrac{4^5.9^4-2.6^9}{2^{10}.3+6^8.20}\)

= \(\dfrac{\left(2^2\right)^5.\left(3^3\right)^4-2.6^9}{2^{10}.3+6^8.20}\)

=\(\dfrac{2^{10}.3^{12}-2.6^9}{2^{10}.3+6^8.20}\)

= \(\dfrac{3^{11}-6}{10}\)

Answer 3

\(A=1+5+5^2+5^3+5^4+...+5^{49}+5^{50}\)

\(\Rightarrow5A=5\left(1+5+5^2+5^3+5^4+...+5^{49}+5^{50}\right)\)

\(\Rightarrow5A=5+5^2+5^3+5^4+5^5+...+5^{50}+5^{51}\)

\(\Rightarrow5A-A=\left(5+5^2+5^3+5^4+5^5+...+5^{50}+5^{51}\right)-\left(1+5+5^2+5^3+5^4+...+5^{49}+5^{50}\right)\)\(\Rightarrow4A=5^{51}-1\)

\(\Rightarrow A=\dfrac{5^{51}-1}{4}\)