tìm x biết:
\(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot101}+...+\frac{1}{10\cdot101}\right)\cdot x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
Những câu hỏi liên quan
Tìm x biết \(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot101}+...+\frac{1}{10\cdot101}\right)\cdot x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
Tìm x biết:
\(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+...+\frac{1}{10\cdot110}\right)\cdot x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
Tìm số nguyên x biết:
\(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+...+\frac{1}{10\cdot110}\right)\cdot x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
Tìm số nguyên x biết:
\(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+...+\frac{1}{10\cdot110}\right)\cdot x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
tìm x
\(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+\frac{1}{3\cdot103}+...+\frac{1}{10\cdot110}\right)\cdot x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
Tìm x
\(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+\frac{1}{3\cdot103}+...+\frac{1}{10\cdot110}\right)\cdot x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
Tính tổng: A=\(\frac{1}{1.101}+\frac{1}{2.102}+\frac{1}{3.103}+...+\frac{1}{10.110}\)
= \(\frac{1}{100}\left(\frac{1}{1}-\frac{1}{101}+\frac{1}{2}-\frac{1}{102}+...+\frac{1}{10}-\frac{1}{110}\right)\)
=\(\frac{1}{100}\left(\left(1+\frac{1}{2}+...+\frac{1}{10}\right)-\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{110}\right)\right)\)(1)
B = \(\frac{1}{10}\left(1-\frac{1}{11}+\frac{1}{2}-\frac{1}{12}+...+\frac{1}{100}-\frac{1}{110}\right)\)
=\(\frac{1}{10}\left(1+\frac{1}{2}+..+\frac{1}{100}-\frac{1}{11}-\frac{1}{12}-...-\frac{1}{110}\right)\)
=\(\frac{1}{10}\left(\left(1+\frac{1}{2}+...+\frac{1}{10}\right)-\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{110}\right)\right)\) (2)
Từ (1) và (2) => x = B/A = 1/10 / 1/100 = 10
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\(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+\frac{1}{3\cdot103}+...+\frac{1}{10\cdot110}\right)\cdot x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
Tìm x bt :
\(\left(\frac{1}{1\cdot101}+\frac{1}{2.102}+....+\frac{1}{10\cdot110}\right)\cdot x=\frac{1}{1.11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
một like cho câu trả lời CHI TIẾT nhất ạ giải phương trình
\(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+\frac{1}{3\cdot103}+...+\frac{1}{10\cdot110}\right)\cdot x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
