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a)
A = 2 + 22 + 23 + 24 + ... + 2200
2A = 22 + 23 + 24 + 25 + ... + 2200
2A - A = A = 2200 - 2
b) chịu
c)
C = 4 + 42 + 43 + 44 +... + 4100
4C = 42 + 43 + 44 + 45 + ... + 4101
4C - C = 3C = 4101 - 4
\(\Rightarrow\) C = \(\frac{4^{101}-4}{3}\)
d)
D = 5 + 52 + 53 + ... + 5100
5D = 52 + 53 + 54 + ... + 5101
5D - D = 4D = 5101 - 5
\(\Rightarrow\)D = \(\frac{5^{101}-5}{4}\)
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c)D=4+42+43+44+...+42012
D=(4+42)+(43+44)+...+(42011+42012)
D=4.5+43.5+45.5+...+42011.5
D=5.(4+43+42011)
=>D chia hết cho 5
=>ĐPCM
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a) \(\frac{\frac{2}{3}+\frac{2}{5}+\frac{2}{9}}{\frac{4}{3}+\frac{4}{5}+\frac{4}{9}}=\frac{2.\left(\frac{1}{3}+\frac{1}{5}+\frac{1}{9}\right)}{4.\left(\frac{1}{3}+\frac{1}{5}+\frac{1}{9}\right)}=\frac{2}{4}=\frac{1}{2}\)
b) \(\frac{\frac{3}{5}+\frac{3}{7}+\frac{3}{9}}{\frac{4}{5}+\frac{4}{7}+\frac{4}{7}}=\frac{3.\left(\frac{1}{5}+\frac{1}{7}+\frac{1}{9}\right)}{4.\left(\frac{1}{5}+\frac{1}{7}+\frac{1}{9}\right)}=\frac{3}{4}\)
43x45=48=65536.
43 x 45 = 43+5= 48