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a.
$S=1+2+2^2+2^3+...+2^{2017}$
$2S=2+2^2+2^3+2^4+...+2^{2018}$
$\Rightarrow 2S-S=(2+2^2+2^3+2^4+...+2^{2018}) - (1+2+2^2+2^3+...+2^{2017})$
$\Rightarrow S=2^{2018}-1$
b.
$S=3+3^2+3^3+...+3^{2017}$
$3S=3^2+3^3+3^4+...+3^{2018}$
$\Rightarrow 3S-S=(3^2+3^3+3^4+...+3^{2018})-(3+3^2+3^3+...+3^{2017})$
$\Rightarrow 2S=3^{2018}-3$
$\Rightarrow S=\frac{3^{2018}-3}{2}$
Câu c, d bạn làm tương tự a,b.
c. Nhân S với 4. Kết quả: $S=\frac{4^{2018}-4}{3}$
d. Nhân S với 5. Kết quả: $S=\frac{5^{2018}-5}{4}$
Bài 1:
1: =15+37+52-37-17=52-2=50
2: =38-42+14-25+27+15=62-42+29=20+29=49
Bài 1: Bỏ ngoặc rồi tính
3) (21-32) - (-12+32)=21-32-(-12)-32=21-32+12-32=-31
4) (12+21) - (23-21+10)=12+21-23+21-10=21
5) (57-725) - (605-53)=57-725-605+53=-1220
6) (55+45+15) - (15-55+45)=55+45+15-15+55-45=55+55=110
Bài 2: Tính các tổng sau một cách hợp lí
1) (-37) + 14 + 26 + 37=(-37+37)+(14+26)=0+40=40
2) (-24) +6 + 10 + 24=(-24+24)+(6+10)=0+16=16
3) 15 + 23 + (-25) + (-23)=(15-25)+(23-23)=-10+0=-10
4) 60 + 33 + (-50) + (-33)=(60-50)+(33-33)=10+0=10
5) (-16) + (-209) + (-14) + 209=(-16-14)+(-209+209)=-30+0=-30
6) (-12) + (-13) + 36 + (-11)=(-11-12-13)+36=-36+36=0
b) 32, 33, 34 , 35.
\(a,2^2=4,2^3=8,2^4=16,2^5=32,2^6=64,2^7=128,2^8=256,2^9=512,2^{10}=1024\)
\(b,3^2=9,3^3=27,3^4=81,3^5=243\)
\(c,4^2=16,4^3=64,4^4=256\)
\(d,5^2=25,5^3=125,5^4=625\)
a)\(...A=\dfrac{2^{50+1}-1}{2-1}=2^{51}-1\)
b) \(...\Rightarrow B=\dfrac{3^{80+1}-1}{3-1}=\dfrac{3^{81}-1}{2}\)
c) \(...\Rightarrow C+1=1+4+4^2+4^3+...+4^{49}\)
\(\Rightarrow C+1=\dfrac{4^{49+1}-1}{4-1}=\dfrac{4^{50}-1}{3}\)
\(\Rightarrow C=\dfrac{4^{50}-1}{3}-1=\dfrac{4^{50}-4}{3}=\dfrac{4\left(4^{49}-1\right)}{3}\)
Tương tự câu d,e,f bạn tự làm nhé
a.SSH : ( 20 - 1 ) : 1 + 1 = 20
tổng : (20 + 1 ) x 20 :2 = 210
b . SSH : (21 - 1) :2 +1 = 11
tổng ; (21 + 1 ) x 11 : 2 = 121
c. SSH : ( 22 - 2 ) : 2 + 1 = 11
tổng : ( 22 + 2) x 11 : 2 = 132
a/ \(=\frac{21}{23}+\frac{125}{143}-\frac{101.21}{101.23}-\frac{1001.125}{1001.143}=0\)
b/ \(=\frac{4}{20}+\frac{8}{21}+\frac{2}{5}-\frac{3}{5}+\frac{2}{21}-\frac{10}{21}+\frac{3}{20}=\frac{7}{20}-\frac{1}{5}=\frac{4}{20}\)
c/ \(\frac{C}{2}=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{420}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{20.21}\)
\(\frac{C}{2}=\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{21-20}{20.21}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{20}-\frac{1}{21}\)
\(\frac{C}{2}=\frac{1}{2}-\frac{1}{21}=\frac{19}{42}\Rightarrow C=\frac{19}{21}\)
a) \(x+5=20-\left(12-7\right)\)
\(\Rightarrow x+5=20-5\)
\(\Rightarrow x+5=15\)
\(\Rightarrow x=15-5\)
\(\Rightarrow x=10\)
b) \(15-\left(3+2x\right)=2^2\)
\(\Rightarrow3+2x=15-4\)
\(\Rightarrow3+2x=11\)
\(\Rightarrow2x=11-3\)
\(\Rightarrow2x=8\)
\(\Rightarrow x=\dfrac{8}{2}\)
\(\Rightarrow x=4\)
c) \(-11-\left(19-x\right)=50\)
\(\Rightarrow19-x=-11-50\)
\(\Rightarrow19-x=-61\)
\(\Rightarrow x=61+19\)
\(\Rightarrow x=80\)
d) \(159-\left(25-x\right)=43\)
\(\Rightarrow25-x=159-43\)
\(\Rightarrow25-x=116\)
\(\Rightarrow x=25-116\)
\(\Rightarrow x=-91\)
e) \(\left(79-x\right)-43=-\left(17-52\right)\)
\(\Rightarrow\left(79-x\right)-43=52-17\)
\(\Rightarrow79-x-43=35\)
\(\Rightarrow36-x=35\)
\(\Rightarrow x=1\)
f) \(\left(7+x\right)-\left(21-13\right)=32\)
\(\Rightarrow7+x-8=32\)
\(\Rightarrow x-1=32\)
\(\Rightarrow x=32+1\)
\(\Rightarrow x=33\)
g) \(-x+20=-15+8+13\)
\(\Rightarrow-x+20=6\)
\(\Rightarrow x=20-6\)
\(\Rightarrow x=14\)
h) \(-\left(-x+13-142\right)+18=55\)
\(\Rightarrow x-13+142+18=55\)
\(\Rightarrow x+147=55\)
\(\Rightarrow x=55-147\)
\(\Rightarrow x=-92\)
13
Bài 1:
a: =42x53+47x42
=42x100
=4200
b: =1152-374-1152-65+374=-65
c: =(-1)+(-1)+...+(-1)+211
=211-105
=106
a) P = 1 + 3 + 3² + ... + 3¹⁰¹
= (1 + 3 + 3²) + (3³ + 3⁴ + 3⁵) + ... + (3⁹⁹ + 3¹⁰⁰ + 3¹⁰¹)
= 13 + 3³.(1 + 3 + 3²) + ... + 3⁹⁹.(1 + 3 + 3²)
= 13 + 3³.13 + ... + 3⁹⁹.13
= 13.(1 + 3³ + ... + 3⁹⁹) ⋮ 13
Vậy P ⋮ 13
b) B = 1 + 2² + 2⁴ + ... + 2²⁰²⁰
= (1 + 2² + 2⁴) + (2⁶ + 2⁸ + 2¹⁰) + ... + (2²⁰¹⁶ + 2²⁰¹⁸ + 2²⁰²⁰)
= 21 + 2⁶.(1 + 2² + 2⁴) + ... + 2²⁰¹⁶.(1 + 2² + 2⁴)
= 21 + 2⁶.21 + ... + 2²⁰¹⁶.21
= 21.(1 + 2⁶ + ... + 2²⁰¹⁶) ⋮ 21
Vậy B ⋮ 21
c) A = 2 + 2² + 2³ + ... + 2²⁰
= (2 + 2² + 2³ + 2⁴) + (2⁵ + 2⁶ + 2⁷ + 2⁸) + ... + (2¹⁷ + 2¹⁸ + 2¹⁹ + 2²⁰)
= 30 + 2⁴.(2 + 2² + 2³ + 2⁴) + ... + 2¹⁶.(2 + 2² + 2³ + 2⁴)
= 30 + 2⁴.30 + ... + 2¹⁶.30
= 30.(1 + 2⁴ + ... + 2¹⁶)
= 5.6.(1 + 2⁴ + ... + 2¹⁶) ⋮ 5
Vậy A ⋮ 5
d) A = 1 + 4 + 4² + ... + 4⁹⁸
= (1 + 4 + 4²) + (4³ + 4⁴ + 4⁵) + ... + (4⁹⁷ + 4⁹⁸ + 4⁹⁹)
= 21 + 4³.(1 + 4 + 4²) + ... + 4⁹⁷.(1 + 4 + 4²)
= 21 + 4³.21 + ... + 4⁹⁷.21
= 21.(1 + 4³ + ... + 4⁹⁷) ⋮ 21
Vậy A ⋮ 21
e) A = 11⁹ + 11⁸ + 11⁷ + ... + 11 + 1
= (11⁹ + 11⁸ + 11⁷ + 11⁶ + 11⁵) + (11⁴ + 11³ + 11² + 11 + 1)
= 11⁵.(11⁴ + 11³ + 11² + 11 + 1) + 16105
= 11⁵.16105 + 16105
= 16105.(11⁵ + 1)
= 5.3221.(11⁵ + 1) ⋮ 5
Vậy A ⋮ 5
A = 20 + 21 + 22 + ... + 22006
2A = 2 + 22 + 23 +...+ 22006 + 22007
2A - A = ( 2 + 22 + 23 + ... + 22006 + 22007 ) - ( 20 + 21 + 22 +...+ 22006 )
A = 22007 - 1
câu b câu d cũng tương tự câu a bạn nhé