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1 + 2 + 3 +...+ 50
Dãy trên có số số hạng là:
\(\left(50-1\right)+1=50\) (số)
Tổng của chúng là:
\(\frac{\left(50+1\right)\cdot50}{2}=1275\)
Vậy tổng của chúng là 1275
~Học tốt~
\(\frac{2}{3}+\frac{14}{15}+\frac{34}{35}+\frac{62}{63}+\frac{98}{99}\)
\(=\frac{3-1}{3}+\frac{15-1}{15}+\frac{35-1}{35}+\frac{63-1}{63}+\frac{99-1}{99}\)
\(=1-\frac{1}{3}+1-\frac{1}{15}+1-\frac{1}{35}+1-\frac{1}{63}+1-\frac{1}{99}\)
\(=5+\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right)\)
\(=5+\frac{1}{2}\left(1-\frac{1}{11}\right)\)
\(=5+\frac{5}{11}=\frac{60}{11}\)
M=1−31+1−151+1−351+1−631+...+1−99991
\(� = \left(\right. 1 + 1 + 1 + . . . + 1 \left.\right) - \left(\right. \frac{1}{3} + \frac{1}{15} + \frac{1}{35} + \frac{1}{63} + . . . + \frac{1}{9999} \left.\right)\)
\(� = \left(\right. 1 + 1 + 1 + . . . + 1 \left.\right) - \left(\right. \frac{1}{1.3} + \frac{1}{3.5} + \frac{1}{5.7} + \frac{1}{7.9} + . . . + \frac{1}{99.101} \left.\right)\)(Có (99 - 1): 2+ 1 = 50 số 1)
\(� = 50 - \frac{1}{2} . \left(\right. \frac{2}{1.3} + \frac{2}{3.5} + \frac{2}{5.7} + \frac{2}{7.9} + . . . + \frac{2}{99.101} \left.\right)\)
\(� = 50 - \left(\right. 1 - \frac{1}{3} + \frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{7} + \frac{1}{7} - \frac{1}{9} + . . . + \frac{1}{99} - \frac{1}{101} \left.\right)\)
\(� = 50 - \left(\right. 1 - \frac{1}{101} \left.\right) = 50 - \frac{100}{101} = \frac{5050 - 100}{101} = \frac{4950}{101}\)
Câu 1: \(\frac{17}{51}\)x \(\frac{45}{30}\)= \(\frac{1}{3}\)x \(\frac{3}{2}\)
= \(\frac{1}{2}\).
Câu 2: \(\frac{24}{15}\)x \(\frac{56}{72}\)x \(\frac{10}{14}\)= \(\frac{8}{5}\)x \(\frac{7}{9}\)x \(\frac{5}{7}\)
= \(\frac{56}{45}\)x \(\frac{5}{7}\)
= \(\frac{8}{9}\)
Câu 3: \(\frac{32}{48}\times\frac{35}{21}\times\frac{63}{14}\times\frac{9}{30}=\frac{2}{3}\times\frac{5}{3}\times\frac{9}{2}\times\frac{3}{10}=\frac{3}{2}\)
k nha
a)17/51x45/40=1/3x3/2=3/6=1/2
b)24/15x56/72x10/14=8/5x7/9x5/7=8/9
c)32/48x35/21x63/14x9/30=2/3x5/3x9/2x3/10=3/2
17/24x15/34=5/16
25/35x14/65=2/13
\(\frac{17}{24}\times\frac{15}{34}=\frac{17\times15}{24\times34}=\frac{5}{16}\)
\(\frac{26}{35}\times\frac{14}{65}=\frac{26\times14}{35\times65}=\frac{4}{25}\)
Học tốt~
\(\frac{17}{24}\)x \(\frac{15}{34}\)= \(\frac{1}{8}\)x \(\frac{5}{2}\)= \(\frac{5}{16}\)
\(\frac{26}{35}\)x \(\frac{14}{65}\)= \(\frac{2}{5}\)x \(\frac{2}{5}\)= \(\frac{4}{25}\)