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\(\left(\frac{123}{100}-\frac{10}{100}-\frac{13}{100}\right).\frac{1}{9}=\)1.1/9=1/9
a. (45-63+18) x (1+2+3+4+5+6+7+8+9)
= 0 x (1+2+3+4+5+6+7+8+9) = 0
b. 60-61+62-63+64-65+66-67+68-69+70
= 60 + (-61-69)+(62+68)+(-63-67)+(64+66)-65+70
= 60 + (-130)+130+(-130)+130-65-70
= 60 + (-130+130) + (-130+130)-65+70
= 60 - 65 + 70 = 65
a:
Số số hạng của dãy số 1;2;3;...;102 là:
\(\frac{102-1}{1}+1=\frac{101}{1}+1=101+1=102\) (số)
1-2+3-4+5-6+...+101-102+103
=(1-2)+(3-4)+(5-6)+...+(101-102)+103
\(=\left(-1\right)+\left(-1\right)+\cdots+\left(-1\right)+103\)
\(=\left(-1\right)\cdot\frac{102}{2}+103=103-51=52\)
b: Sửa đề: 2-4+6-8+10-12+...+98-100+102
Số số hạng của dãy số 2;4;6;8;...;98;100 là:
\(\frac{100-2}{2}+1=\frac{98}{2}+1=49+1=50\) (số)
2-4+6-8+10-12+...+98-100+102
=(2-4)+(6-8)+(10-12)+...+(98-100)+102
=(-2)+(-2)+...+(-2)+102
\(=-2\cdot\frac{100}{2}+102\)
=-100+102
=2
c: Số số hạng trong dãy 16;18;20;22;...;64;66 là:
\(\frac{66-16}{2}+1=\frac{50}{2}+1=25+1=26\) (số)
16-18+20-22+...+64-66+68
=(16-18)+(20-22)+...+(64-68)+68
=(-2)+(-2)+...+(-2)+68
\(=\left(-2\right)\cdot\frac{26}{2}+68\)
=68-13
=55
a; \(\dfrac{1}{4}\) + \(\dfrac{2}{5}\) + \(\dfrac{6}{8}\) + \(\dfrac{9}{15}\) + \(\dfrac{8}{1}\)
= (\(\dfrac{1}{4}\) + \(\dfrac{6}{8}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{9}{15}\)) + \(\dfrac{8}{1}\)
= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + 8
= 1 + 1 + 8
= 2 + 8
= 10
b; \(\dfrac{1}{2}\) + \(\dfrac{2}{4}\) + \(\dfrac{3}{6}\) + \(\dfrac{4}{8}\) + \(\dfrac{5}{10}\) + \(\dfrac{6}{12}\) + \(\dfrac{7}{14}\) + \(\dfrac{8}{16}\) + \(\dfrac{10}{20}\)
= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (\(\dfrac{2}{2}\) + \(\dfrac{3}{3}\) + \(\dfrac{4}{4}\) + \(\dfrac{5}{5}\)+ \(\dfrac{6}{6}+\dfrac{7}{7}+\dfrac{8}{8}\) + \(\dfrac{10}{10}\))
= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (1 + 1 +1 + 1+ 1+ 1+ 1 +1)
= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x 1 x 8
= \(\dfrac{1}{2}\) + \(\)\(\dfrac{1}{2}\) x 8
= \(\dfrac{1}{2}\) + 4
= \(\dfrac{9}{2}\)
a; \(\dfrac{1}{4}\) + \(\dfrac{2}{5}\) + \(\dfrac{6}{8}\) + \(\dfrac{9}{15}\) + \(\dfrac{8}{1}\)
= (\(\dfrac{1}{4}\) + \(\dfrac{6}{8}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{9}{15}\)) + 8
= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + 8
= 1 + 1 + 8
= 2 + 8
= 10
b; \(\dfrac{1}{2}\) + \(\dfrac{2}{4}\) + \(\dfrac{3}{6}\) + \(\dfrac{4}{8}\) + \(\dfrac{5}{10}\) + \(\dfrac{6}{12}\) + \(\dfrac{7}{14}\) + \(\dfrac{8}{16}\) + \(\dfrac{9}{18}\) + \(\dfrac{10}{20}\)
= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\)
= \(\dfrac{1}{2}\) x 10
= 5