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Em nhân từng phân số với \(\frac{1}{7}\)
\(\frac{1}{7}P=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}+\frac{15}{28.43}+\frac{13}{43.56}\)
\(\frac{1}{7}P=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{43}-\frac{1}{56}\)
\(\frac{1}{7}P=\frac{1}{2}-\frac{1}{56}\)
\(\frac{1}{7}P=\frac{27}{56}\)
\(P=\frac{27}{56}:\frac{1}{7}\)
\(P=\frac{27}{8}>3\)
Vậy P >3
( ko hiểu chỗ nào thì hỏi nhá )
\(P=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}+\frac{15}{4.43}+\frac{13}{43.8}\)
\(\Leftrightarrow\)\(\frac{1}{7}P=\frac{1}{7}\left(\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}+\frac{15}{4.43}+\frac{13}{43.8}\right)\)
\(=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}+\frac{15}{28.43}+\frac{13}{43.56}\)
\(=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}+\frac{1}{28}-\frac{1}{43}+\frac{1}{43}-\frac{1}{56}\)
\(=\frac{1}{2}-\frac{1}{56}=\frac{27}{56}\)
\(\Leftrightarrow\)\(P=\frac{27}{56}:\frac{1}{7}=3\frac{3}{8}\)\(>3\) (ĐPCM)
\(B=\dfrac{5}{2.1}+\dfrac{4}{1.11}+\dfrac{3}{11.2}+\dfrac{1}{2.15}+\dfrac{13}{15.4}\)
\(\dfrac{B}{7}=\dfrac{5}{2.7}+\dfrac{4}{7.11}+\dfrac{3}{11.14}+\dfrac{1}{14.15}+\dfrac{13}{15.4}\)
\(\dfrac{B}{7}=\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{7}{11}+...+\dfrac{1}{15}-\dfrac{1}{28}\)
\(\dfrac{B}{7}=\dfrac{1}{2}-\dfrac{1}{28}\)
\(\dfrac{B}{7}=\dfrac{13}{28}\)
\(B=\dfrac{13}{28}.7=\dfrac{13}{4}\)
* Bỏ ngoặc vuông đi :(
\(\text{Ta có:}\)
\(200-\left(3+\frac{2}{3}+\frac{2}{4}+...+\frac{2}{100}\right)\)
\(\rightarrow200-2-\left(1+\frac{2}{3}+...+\frac{2}{100}\right)\)
\(\rightarrow198-\left(1+\frac{2}{3}+...+\frac{2}{100}\right)\)
\(\rightarrow198-\left(1+\frac{2}{3}+...+\frac{2}{100}\right)\)
\(\rightarrow2.[99-\left(\frac{1}{2}-\frac{1}{3}+...+\frac{1}{100}\right)]\) \(\left(1\right)\)
\(\text{Ta có:}\)
\(\frac{1}{2}+\frac{2}{3}+...+\frac{99}{100}\)
\(\text{Rút}\)\(\left(1\right)\)\(\text{ra có 99 số}\)
\(\rightarrow99-\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)\) \(\left(2\right)\)
\(\text{Từ}\)\(\left(1\right)\)\(\text{và}\)\(\left(2\right)\)\(\Rightarrow\)\(200-\left(3+\frac{2}{3}+\frac{2}{4}+\frac{2}{5}+...+\frac{2}{100}\right):\left(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{99}{100}\right)=2\)
A= (21+22+23)+(24+25+26)+...+(258+259+260)
=20(21+22+23)+23(21+22+23)+...+257(21+22+23)
=(21+22+23)(20+23+...+257)
= 14(20+23+...+257) chia hết cho 7
Vậy A chia hết cho 7
gọi 1/41+1/42+1/43+...+1/80=S
ta có :
S>1/60+1/60+1/60+...+1/60
S>1/60 x 40
S>8/12>7/12
Vậy S>7/12