a)
Đặt:
\(A=1-2+2^2-2^3+...+2^{2022}\\ 2A=2-2^2+2^3-2^4+...+2^{2023}\\ 2A+A=\left(2-2^2+2^3-2^4+...+2^{2023}\right)+\left(1-2+2^2-2^3+...+2^{2022}\right)\\ 3A=2^{2023}-1\\ A=\dfrac{2^{2023}-1}{3}\)
b)
Đặt:
\(B=1+3+3^2+3^3+...+3^{2022}\\ 3B=3+3^2+3^3+3^4+...+3^{2023}\\ 3B-B=\left(3+3^2+3^3+3^4+...+3^{2023}\right)-\left(1+3+3^2+...+3^{2022}\right)\\ 2B=3^{2023}-1\\ B=\dfrac{3^{2023}-1}{2}\)
2023-1/2*(1+2)-1/3*(1+2+3)-1/4*(1+2+3+4)-...-1/2022*(1+2+3+4+...+2022)
cho tổng
M = 1/3+ 2/3^2+3/3^3+.....+ 2022/3^2022+ 2023/3^2023
So sánh M với 3/4
tính A=1/2!+2/3!+3/4!+...+2021/2022!
1) thực hiện phép tính a)5-(1+1/3):(1-1/3) b)(1+2/3-5/4)-(1-5/4)+2022-2/3 2) Tìm x biết a) 0,7²×X=0,49² b)X:(-0,5)³=(0,5)²
1. So sánh
a) \(A=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2020}}+\dfrac{1}{2^{2021}}\) và B= \(\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{13}{60}\)
b) \(C=\dfrac{2019}{2021}+\dfrac{2021}{2022}\) và \(D=\dfrac{2020+2022}{2019+2021}.\dfrac{3}{2}\)
B=1/2-1/2^2+1/2^3-1/2^4+..... -1/2^2022+1/2^2023
Thu gọn B
\(\dfrac{\dfrac{2022}{1}+\dfrac{2021}{2}+\dfrac{2020}{3}+...+\dfrac{1}{2022}}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2023}}\)
Giúp mình câu này với ạ
A= \(1-3+3^2-3^3+...+3^{2022}-\dfrac{3^{2023}}{4}\)
C=1-2+2^2-2^3+2^4-...+2^2022
1 - 3 + 3 mũ 2 - 3 mũ 3 + 3 mũ 4 - ...... + 3 mũ 2022 - 3 mũ 2023 phần 4
