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M = 5 + 53 + 55 + ... + 547 + 549
52M = 52(5 + 53 + 55 + ... + 547 + 549)
25M = 53 + 55 + 57 + ... + 549 + 551
25M - M = ( 53 + 55 + 57 + ... + 549 + 551) - (5 + 53 + 55 + ... + 547 + 549)
24M = 551 - 5
M = \(\frac{5^{51}-5}{24}\)

P = 2\(x\)3 + 3\(x\)2 + 4\(x\) + 5
Thay \(x\) = 3 vào P ta có:
P = 2.33 + 3.32 + 4.3 + 5
P = 54 + 27 + 12 + 5
P = 98

A = ( -4/5 + 4/3 ) + (-5/4 + 14/5) - 7/3
= 8/15 + 31/20 - 7/3
= 25/12 - 7/3
= -1/4
B = 8/3 x 2/5 x 3/8 x 10x 19/92
= 16/15 x 15/4 x 19/92
= 4x19/92
= 19/23
C = - \(\dfrac{5}{7}\) x \(\dfrac{2}{11}\) + \(\dfrac{-5}{7}\) x \(\dfrac{9}{14}\) + \(\dfrac{1}{57}\)
= - \(\dfrac{10}{77}\) - \(\dfrac{45}{98}\) + \(\dfrac{1}{57}\)
= - \(\dfrac{635}{1078}\) + \(\dfrac{1}{57}\)
= - \(\dfrac{36195}{61446}\) + \(\dfrac{1078}{61446}\)
= - \(\dfrac{35117}{61446}\)

\(S=\frac{3}{\left(1\times2\right)^2}+\frac{5}{\left(2\times3\right)^2}+...+\frac{201}{\left(100\times101\right)^2}\)
\(=\frac{2^2-1^2}{\left(1\times2\right)^2}+\frac{3^2-2^2}{\left(2\times3\right)^2}+...+\frac{101^2-100^2}{\left(100\times101\right)^2}\)
\(=\frac{1}{1^2}-\frac{1}{2^2}+\frac{1}{2^2}-\frac{1}{3^2}+...+\frac{1}{100^2}-\frac{1}{101^2}\)
\(=1-\frac{1}{101^2}\)
\(=\frac{10200}{10201}\)


a) \(\frac{3}{40}+\frac{5}{3}+\frac{7}{60}=\frac{9}{120}+\frac{200}{120}+\frac{14}{120}=\frac{223}{120}\)
b) \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{19.20}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{19}-\frac{1}{20}=1-\frac{1}{20}=\frac{19}{20}\)

a)(9x+2)x3=60
9x+2 =60:3
9x+2 =20
9x =20-2
9x=18
x=18:9
x=2
2
3/5 : 3/10 = 3/5 x 10/3 = 2