Question

Tính nhanh tổng sau :P = 3/2 + 3/8 + 3/32 + 3/128 + 3/512

Answer 1

\(P+\frac{1}{512}=\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{4}{512}=\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{4}{128}=\)

\(=\frac{3}{2}+\frac{3}{8}+\frac{4}{32}=\frac{3}{2}+\frac{4}{8}=\frac{4}{2}=2\)

\(\Rightarrow P=2-\frac{1}{512}=\frac{1023}{512}\)

Answer 2

\(P=\frac{3}{2}+\frac{3}{8}+...+\frac{3}{512}\)

\(=3.\left(\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}+\frac{1}{2^9}\right)\)

\(4P=3\left(\frac{1}{2^3}+\frac{1}{2^5}+...+\frac{1}{2^{11}}\right)\)

\(4P-P=3\left(\frac{1}{2}-\frac{1}{2^{11}}\right)\)

\(3P=3\left(\frac{1}{2}-\frac{1}{2^{11}}\right)\)

\(P=\frac{1}{2}-\frac{1}{2^{11}}=\frac{2^{10}-1}{2^{11}}\)

Answer 3

Đinh Thùy LinhTính nhanh mà bạn cách này mk nhanh hơn nhiều :D

Answer 4

ô Dung nhanh quá cách mk giống cah DUng đấy :D

Answer 5

Chết r nhầm

Answer 6

Tui nhầm phải nhân với \(\frac{1}{4}\)

Answer 7

Ông Thắng nếu làm thế kia thì sai r tui làm lại đây

Answer 8

\(P=3\left(\frac{1}{2}+\frac{1}{2^3}+...+\frac{1}{2^9}\right)\)

\(\frac{1}{4}P=3\left(\frac{1}{2^3}+\frac{1}{2^5}+\frac{...1}{2^{11}}\right)\)

\(P-\frac{1}{4}P=3\left(\frac{1}{2}-\frac{1}{2^{11}}\right)\)

\(\frac{3}{4}P=3\left(\frac{1}{2}-\frac{1}{2^{11}}\right)\)

\(P=\left(\frac{1}{2}-\frac{1}{2^{11}}\right).4\)

\(=\frac{2^{10}-1}{2^9}\)