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a: Số số hạng là n-1+1=n(số)
Tổng là n(n+1)/2
b: Số số hạng là (2n-1-1):2+1=(2n-2)/2+1=n(số)
Tổng là:
\(\dfrac{\left(2n-1+1\right)\cdot n}{2}=n^2\)
c: Số số hạng là (2n-2):2+1=n(số)
Tổng là \(\dfrac{\left(2n+2\right)\cdot n}{2}=n\left(n+1\right)\)
d: SỐ số hạng là (51-5)/5+1=11(số)
Tổng là \(\dfrac{\left(51+1\right)\cdot11}{2}=26\cdot11=286\)
Bài 2:
a: \(\dfrac{4\cdot7}{9\cdot32}=\dfrac{4}{32}\cdot\dfrac{7}{9}=\dfrac{1}{8}\cdot\dfrac{7}{9}=\dfrac{7}{72}\)
b: \(\dfrac{3\cdot21}{14\cdot15}=\dfrac{63}{210}=\dfrac{3}{10}\)
c: \(\dfrac{9\cdot6-9\cdot3}{18}=\dfrac{9\cdot3}{18}=\dfrac{3}{2}\)
d: \(\dfrac{17\cdot15-17}{3-20}=\dfrac{17\cdot14}{-17}=-14\)
e: \(=\dfrac{26\cdot5}{26\cdot35}=\dfrac{5}{35}=\dfrac{1}{7}\)
f: \(=\dfrac{49\left(1+7\right)}{49}=8\)
a: \(=\dfrac{-1}{4}+\dfrac{7}{33}-\dfrac{5}{3}-\dfrac{5}{4}-\dfrac{6}{11}+\dfrac{48}{49}\)
\(=\dfrac{-3}{2}+\dfrac{7}{33}-\dfrac{18}{33}-\dfrac{5}{3}+\dfrac{48}{49}\)
\(=\dfrac{-9-10}{6}+\dfrac{-11}{33}+\dfrac{48}{49}\)
\(=\dfrac{-19}{6}+\dfrac{-1}{3}+\dfrac{48}{49}=-\dfrac{247}{98}\)
b: \(=\dfrac{11}{125}-\dfrac{17}{18}+\dfrac{4}{9}-\dfrac{5}{7}+\dfrac{17}{14}\)
\(=\dfrac{11}{125}+\dfrac{-17+8}{9}+\dfrac{-10+17}{14}\)
\(=\dfrac{11}{125}-1+\dfrac{7}{14}=\dfrac{11}{125}+\dfrac{1}{2}=\dfrac{22+125}{250}=\dfrac{147}{250}\)
a) = -29+29+61-31=30
b) = 131-93-16-131+93+4=12
c) = 0-1-3-5-7-...-49-51=-667
a, \(\dfrac{10}{17}\) + \(\dfrac{5}{-13}\) - \(\dfrac{11}{25}\) + \(\dfrac{7}{17}\) - \(\dfrac{8}{13}\)
= ( \(\dfrac{10}{17}\) + \(\dfrac{7}{17}\)) - ( \(\dfrac{5}{13}\) + \(\dfrac{8}{13}\)) - \(\dfrac{11}{25}\)
= \(\dfrac{17}{17}\) - \(\dfrac{13}{13}\) - \(\dfrac{11}{25}\)
= 1 - 1 - \(\dfrac{11}{25}\)
= - \(\dfrac{11}{25}\)
b, 0,3 - \(\dfrac{93}{7}\) - 70% - \(\dfrac{4}{7}\)
= 0,3 - 0,7 - ( \(\dfrac{93}{7}+\dfrac{4}{7}\))
= - 0,4 - \(\dfrac{97}{7}\)
= - \(\dfrac{2}{5}\) - \(\dfrac{97}{7}\)
= - \(\dfrac{499}{35}\)
a) \(5^4:\left(2x-1\right)^2=25\\ \Leftrightarrow5^4:\left(2x-1\right)^2=5^2\\ \Leftrightarrow5^4:5^2=\left(2x-1\right)^2\\ \Leftrightarrow\left[{}\begin{matrix}\left(2x-1\right)^2=5^2\\\left(2x-1\right)^2=\left(-5\right)^2\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}2x-1=5\\2x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
b) \(17^3.x=17^4\\ \Rightarrow x=17^4:17^3=17\)
c) \(\left(2x+1\right)^3:49=7\\ \Leftrightarrow\left(2x-1\right)^3:7^2=7\\ \Leftrightarrow\left(2x-1\right)^3=7.7^2=7^3\\ \Leftrightarrow2x-1=7\\ \Leftrightarrow x=4\)
a)54 : (2x - 1)2 =25
54 : (2x - 1)2 =52
(2x - 1)2 =54 : 52
(2x - 1)2 = 52
2x - 1 = 5
2x = 5+1
2x = 6
x = 6: 2
x = 3
b)173.x = 174
x = 174 : 173
x = 17
c)(2x + 1)3 : 49 =7
(2x + 1)3 = 7 . 49
(2x + 1)3 = 343
(2x + 1)3 = 73
2x +1 = 7
2x = 7- 1
2x = 6
x = 6:2
x = 3
a.17 . 85 + 25 . 17 + 1200
=17.(85+25)+1200
=17.110+1200
=1870+1200
=3070
b.62 : 4 . 3 + 2 . 52
=36:4.3+2.25
=27+50
=77
c.5 . 42 - 18 : 32
=5.16-18:9
=80-2
=78
d.3 . 52 - 16 : 23 + 34 : 33
=3.25-16:8+3
=75-2+3
=76
e.220 - [ 32 . 33 - ( 12 - 70 ) 2]
=220-35+112
=220-243+121
=98
j. 49 . 73 + 49 . 51 - 49 . 24
=49.(73+51-24)
=49.100
=4900
Con bấm mỏi suốt đấy mấy má
nhầm
a) 17 . 85 + 25 . 17 + 1200
=(17.85+25.17)+1200
=17(85+25)+1200
=17.110+1200
=1870+1200
=3070
b) 62 : 4 . 3 + 2 . 52
=36:4.3+2.25
=9.3+50
=27+50
=77
c) 5 . 42 - 18 : 32
=5.16-18:9
=80-2
=78
d) 3 . 52 - 16 : 23 + 34 : 33
=3.25-24:23+3(4-3)
=75-2(4-3)+31
=75-21+3
=75-2+3
=76
e) 220 - [ 32 . 33 - ( 12 - 70 ) 2 ]
=220-[3(2+3)-(12-1)2]
=220-(35-112)
=220-(243-121)
=220-122
=98
j) 49 . 73 + 49 . 51 - 49 . 24
=49(73+51-24)
=49.100
=4900
a) A = 2 + 22 + 23 +...+ 229
=>2A= 22 + 23 +...+ 230
=>2A-A= 22 + 23 +...+ 230-2-22-23-...-229
=>A.(2-1)=230-2
=>A=230-2
b) B = 1 + 3 + 32 + 33 + ... + 339
=>3B=3 + 32 + 33 + ... + 340
=>3B-B=3 + 32 + 33 + ... + 340-1 - 3 - 32 - 33 - ... - 339
=>B(3-1)=340-1
=>B.2=340-1
=>B=\(\frac{3^{40}-1}{2}\)
nhiều wa 2 câu trước
a) A= 2 + 2^2 + 2^3 + ... + 2^29
2A= 2. (2 + 2^2 + 2^3 + ... + 2^29)
2A= 2^2 + 2^3 + 2^4 + ... +2^29 + 2^30
- (dấu trừ viết ra đầu dòng nha)
A= 2 + 2^2 + 2^3 + 2^4 ... + 2^29
1A= 2^29 - 2
A= 2^29 -2 trên 1
kick mk nha
Đáp án là A