Question

[Nguyễn Thị Thu Hà]

tính nhanh tổng sau :

a, D=1/2+1/4+1/8+1/16+1/32+•••+1/512+1/1024

b, Đ=1/1*2+1/2*3+1/3*4+•••+1/18*19+1/19*20

c,E=1/11*16+1/16*21+1/21*26+•••1/56*26+1/61*-6

Ai nhanh thì mình tick

Answer 1

[Không Tên]

a)   \(D=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+...+\frac{1}{512}+\frac{1}{1024}\)

=>  \(2D=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...++\frac{1}{256}+\frac{1}{512}\)

=>  \(2D-D=\left(1+\frac{1}{2}+...+\frac{1}{512}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\right)\)

=>  \(D=1-\frac{1}{1024}\)

b)  \(Đ=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}+\frac{1}{19.20}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\)

\(=1-\frac{1}{20}=\frac{19}{20}\)

Answer 2

[Con Ma]

a) D=\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\dots+\frac{1}{512}+\frac{1}{1024}.\) 

\(D=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\dots+\frac{1}{512}-\frac{1}{1024}\)

\(D=1-\frac{1}{1024}\)

\(D=\frac{1023}{1024}\)

\(Đ=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\dots+\frac{1}{18\cdot19}+\frac{1}{19\cdot20}\)

\(Đ=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\dots+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\)

\(Đ=1-\frac{1}{20}\) 

\(Đ=\frac{19}{20}\)

Phần c như kiểu sai đề chỗ cuối hay sao ấy.