\(\frac{198\cdot199-200}{198\cdot197-200}\)
\(y=\frac{198\cdot199-200}{196+197\cdot198}\)
\(\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{200}}{\frac{1}{199}+\frac{2}{198}+....+\frac{198}{2}+\frac{199}{1}}\)
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tính
\(\frac{\frac{1}{2}+\frac{1}{3}+....+\frac{1}{200}}{\frac{1}{199}+\frac{2}{198}+.....+\frac{198}{1}+\frac{199}{1}}\)
Tính: \(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{200}}{\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{198}{2}+\frac{199}{1}}\)
\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{200}}{\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{198}{2}+\frac{199}{1}}\)
\(=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{200}}{\left(\frac{1}{199}+1\right)+\left(\frac{2}{198}+1\right)+\left(\frac{3}{197}+1\right)+...+\left(\frac{198}{2}+1\right)+1}\)
\(=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{200}}{\frac{200}{199}+\frac{200}{198}+\frac{200}{197}+...+\frac{200}{2}+\frac{200}{200}}\)
\(=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{200}}{200\cdot\left(\frac{1}{200}+\frac{1}{199}+\frac{1}{198}+\frac{1}{197}+...+\frac{1}{2}\right)}\)
\(=\frac{1}{200}\)
Số nguyên x thỏa mãn:x=(-199)=-1
A.x=198 B.x=200 C.x=200 D.x=-198
help me!!!
Lời giair:
$x+(-199)=-1$
$x=-1-(-199)=-1+199=199-1=198$
Đáp án A.
Rút gọn:
\(A=\frac{200+\frac{199}{2}+\frac{198}{3}+...+\frac{2}{199}+\frac{1}{200}}{\frac{100}{2}+\frac{100}{3}+...+\frac{100}{200}+\frac{100}{201}}\)
198*199-200/196+197*198
198*199-200/196+197*198
cho A = 1/199+2/198+3197+...+198/2+199/1.Chứng minh A = 200.(1/2+1/3+...+1/200)
\(A=\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{189}{2}+\frac{199}{1}\)
\(A=\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{198}{2}+199\)
\(A=\left(\frac{1}{199}+1\right)+\left(\frac{2}{198}+1\right)+\left(\frac{3}{197}+1\right)+...+\left(\frac{198}{2}+1\right)+1\)
\(A=\frac{200}{199}+\frac{200}{198}+\frac{200}{197}+...+\frac{200}{2}+1\)
\(A=\frac{200}{200}+\frac{200}{199}+\frac{200}{198}+\frac{200}{197}+...+\frac{200}{2}\)
\(A=200\left(\frac{1}{200}+\frac{1}{199}+\frac{1}{198}+...+\frac{1}{2}\right)\)
Vậy \(A=200\left(\frac{1}{200}+\frac{1}{199}+\frac{1}{198}+...+\frac{1}{2}\right)\)