\(\frac{1}{2}+\frac{1}{8}+\frac{1}{32}.......\frac{1}{56}+\frac{1}{60}\)
Hãy tính tổng trên
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
20 tháng 2 2017
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{56}=\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}...\frac{1}{7x8}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}\)\(-\frac{1}{8}=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)
b,
13 tháng 7 2018
\(A=-\frac{1}{20}+-\frac{1}{30}+-\frac{1}{42}+-\frac{1}{56}+-\frac{1}{72}+-\frac{1}{90}\)
\(\Rightarrow A=-1\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{9.10}\right)\)
\(A=-1\left(\frac{1}{4}-\frac{1}{10}\right)\)
\(\Rightarrow A=-\frac{3}{20}\)
D
13 tháng 7 2018
\(A=\frac{-1}{20}-\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)
\(A=-\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(A=-\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(A=-\left(\frac{1}{4}-\frac{1}{10}\right)\)
\(A=\frac{-3}{20}\)
#
25 tháng 3 2016
A= \(\frac{-1}{4\cdot5}+\frac{-1}{5\cdot6}+\frac{-1}{6\cdot7}+\frac{-1}{7\cdot8}+\frac{-1}{8\cdot9}+\frac{-1}{9\cdot10}\)
=\(-1\left(\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\right)\)
=\(-1\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}\right)\)
=\(-1\left(\frac{1}{4}-\frac{1}{10}\right)\)
=\(-1\cdot\frac{3}{20}\)
=\(\frac{-3}{20}\)
=\(\frac{-1}{20}\)
27 tháng 3 2017
\(\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90} \)\(\frac{-1}{90}\)
\(=\frac{-1}{4.5}+\frac{-1}{5.6}+\frac{-1}{6.7}+\frac{-1}{7.8}+\frac{-1}{8.9}+\frac{-1}{9.10}\)
\(=\frac{-1}{4}-\frac{-1}{5}+\frac{-1}{5}-\frac{-1}{6}+\frac{-1}{6}-\frac{-1}{7}+\frac{-1}{7}-\frac{-1}{8}+\frac{-1}{8}-\frac{-1}{9}+\frac{-1}{9}-\frac{-1}{10}\)
\(=\frac{-1}{4}-\frac{-1}{10} \)\(=\frac{-3}{20}\)
PV
27 tháng 3 2017
\(\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)
= \(\frac{-1}{4}-\frac{-1}{10}\)
=\(\frac{-3}{20}\)
24 tháng 7 2016
Đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)
\(A=1-\frac{1}{64}=\frac{63}{64}\)
24 tháng 7 2016
Ta thấy: 1/2 = 1 - 1/2
1/2 + 1/4 = 3/4 = 1- 1/4
1/2 + 1/4 + 1/8 = 7/8 = 1 - 1/8
Tương tự ta có:
1/2 + 1/4 +1/8 + 1/16 + 1/32 + 1/64 = 1 - 1/64 = 63/64
S
2 tháng 5 2017
a, \(1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}.......1\frac{1}{99}\)
\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}......\frac{10^2}{9.11}\)
\(=\frac{\left(2.3.4......10\right)\left(2.3.4....10\right)}{\left(1.2.3....9\right)\left(3.4.5....11\right)}\)
\(=\frac{10.2}{1.11}=\frac{20}{11}\)
b, Gọi A = \(\frac{31}{2}\cdot\frac{32}{2}\cdot\frac{33}{2}\cdot\cdot\cdot\cdot\frac{60}{2}\),gọi B = \(1.3.5....59\)
Ta có: \(A=\frac{31}{2}.\frac{32}{2}.\frac{33}{2}.....\frac{60}{2}\)
\(=\frac{31.32.33....60}{2^{30}}\)
\(=\frac{\left(31.32.33.....60\right)\left(1.2.3....30\right)}{2^{30}.\left(1.2.3....30\right)}\)
\(=\frac{1.2.3.....60}{\left(2.1\right)\left(2.2\right)\left(2.3\right)....\left(2.30\right)}\)
\(=\frac{1.2.3.....60}{2.4.6....60}\)
\(=\frac{\left(1.3.5...59\right)\left(2.4....60\right)}{2.4.6...60}\)
\(=1.3.5....59=B\)
Vậy A = B