Tính tổng : S\(_1\) = \(1+3^2+5^2+7^2+....+97^2+99^2\)
S\(_2\) =\(2+4^2+6^2+8^2+.....+98^2+100^2\)
S\(_3\) = 1.2.3+2.3.4+3.4.5+....+97.98.99
Bài 1. Tính các tổng sau:
1. S= 1+2+3+4+.................+98+99+100
2. S= 2+4+6+8+.................+996+998
3. S= 1.2+2.3+3.4+.............+98.99+99.100
4. S= 1.2.3+2.3.4+3.4.5+..............+97.98.99+98.99.100
5. S= 1+2+3+..........+98+99+100
AI NHANH MIK TICK NHA MN ƠI
Bài 1. Tính các tổng sau:
1. S= 1+2+3+4+.................+98+99+100
S=( 100 - 1 ): 1 + 1 = 100
2. S= 2+4+6+8+.................+996+998
S = ( 998 - 2 ) : 2 + 1 = 499
3. S= 1.2+2.3+3.4+.............+98.99+99.100
S= 1.2 3-0 +2.3 (4-1) +3.4
4. S= 1.2.3+2.3.4+3.4.5+..............+97.98.99+98.99.100
S= (100 -1) + 1 : 1 = 100
5. S= 1+2+3+..........+98+99+100
S=( 100 - 1) + 1 : 1
S= 100
1.S=(1+100)+(2+99)+...(50+51) (Tổng cộng có 50 cặp)
S=101+101+101+...101
S=101 x 50=5050
=>S= 5050
ღ๖ۣۜChâu 's ngốcღ๖ۣۜ 101 câu 1 ở đâu vậy ? 50 ở đâu vậy ?
tính tổng: a> A=2^100-2^99+2^98-2^97+...+2^2-2
b> B=1/1.2.3+1/2.3.4+1/3.4.5+.....+1/2015.2016.2017
Câu a)
\(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)
\(=\left(2^{100}+2^{99}+2^{98}+2^{97}+...+2^2+2\right)-2\left(2^{99}+2^{97}+2^{95}+...+2^3+2\right)\)
\(=\left(2^{100}+2^{99}+2^{98}+2^{97}+...+2^2+2\right)-\left(2^{100}+2^{98}+2^{96}+...+2^4+2^2\right)\)
\(=2^{99}+2^{97}+2^{95}+...+2^3+2\)
\(=\frac{2^2\cdot\left(2^{99}+2^{97}+2^{95}+...+2^3+2\right)-\left(2^{99}+2^{97}+2^{95}+...+2^3+2\right)}{3}\)
\(=\frac{\left(2^{101}+2^{99}+2^{97}+...+2^5+2^3\right)-\left(2^{99}+2^{97}+2^{95}+...+2^3+2\right)}{3}\)
\(=\frac{2^{101}-2}{3}\)
\(2B=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{2015.2016.2017}\)
\(2B=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{2.4}+...+\frac{1}{2015.2016}-\frac{1}{2016.2017}\)
\(2B=\frac{1}{1.2}-\frac{1}{2016.2017}\)
\(B=\frac{\frac{1}{1.2}-\frac{1}{2016.1017}}{2}\)
Bài 1: Tính tổng các dãy số sau.
a. S= 1+2+3+4+.....+98+99+100
b. S= 2+4+6+8+.....+996+998
c. S= 1.2+2.3+3.4+.....+98.99+99.100
d. S= 1.2.3+2.3.4+3.4.5+......+97.98.99+98.99.100
e. S= 12+22+32+.....982+992+1002
GIÚP MIK NHA , MIK CẦN GẤP, AI NHANH MIK TICK
a. Áp dụng CT: n.9n+1)/2
=>S=(101.100)/2
b. SSH=(998-2) : 2+1
TBC=(998+2):2
Nhân SSH với TBC => S
c.
Đặt A= 1.2 + 2.3 + 3.4 + ...+ 99.100
3A = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3A= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
3A= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
3A = 99.100.101 3S = 3.33.100.101
A=33.100.101= 333300
d.
Đặt A=1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100
4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100)4
4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)
4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100
4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98.99.100.101
4A=98.99.100.101
=>A=98.99.100.101/4
a. S= 1+2+3+4+.....+98+99+100
S= (100 -1) : 1 + 1 =100
b. S= 2+4+6+8+.....+996+998
S= (998 - 2 ) : 2 + 1 = 499
c. S= 1.2+2.3+3.4+.....+98.99+99.100
Bài này hôm qua đã làm -.- vào thống kê của tôi mà nhìn :)
d. S= 1.2.3+2.3.4+3.4.5+......+97.98.99+98.99.100
S = (1.2.3.2.3.4.5.4.5.6+98.99.100)4
S=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+97.98.99+98.99.100
S=101 - 97
S=1.2.3.5.2.4.+2.1.2.3.4.3.4.5.5.6-2.4.5.4.5.6.7-3.4.5.6-3.4.5.6+.......100
S=1.2.3.3.4.5.5.6.7.7.8.9......+97.98.99+98.99.100
S=1.2.3.4.4.3.2.1+2.3.5-2.3.4.5+3.4.5.6.6.7.3.4.5.6+........97.98.99+98.99.100
S= 98.99.100.101
S=98.99.100.\(\frac{101}{4}\)
e. S= 12+22+32+.....982+992+1002
S= 1002 - 992 + 982 -972 +...+ 22- 12
S= (100 - 99) (100+99) (98 - 97) (98+97) +....+(2-1) (2+1)
S=(1+100) 100 :2
s=5050
Bài 1. Tính tổng các dãy số sau :
a. S= 1+2+3+......+100
b. S= 2+4+6+.....+998
c. S= 1.2+2.3+3.4+......+98.99+99.100
d. S= 1.2.3+2.3.4+3.4.5+......+98.99.100
e. S= 12+22+32+......+992+1002
a)S có số số hạng là:
(100-1):1+1=100(số hạng)
Vậy S bằng:
(1+100)X100:2=5050
b)S có số số hạng là:
(998-2):2+1=499(số hạng)
Vậy S bằng:
(2+998)X499:2=249500
c)S=1.2+2.3+3.4+...+98.99+99.100
3S=1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3S=1.2.3+2.3.(4-1)+3.4.(5-2)+...+98.99.(100-97)+99.100.(101-98)
3S=1.2.3+(2.3.4-1.2.3)+(3.4.5-2.3.4)+...+(98.99.100-97.98.99)+(99.100.101-98.99.100)
3S=(1.2.3+2.3.4+3.4.5+...+98.99.100+99.100.101)-(1.2.3+2.3.4+3.4.5+...+97.98.99+98.99.100)
3S=99.100.101=999900
S=333300
d)S=1.2.3+2.3.4+...+98.99.100
4S=1.2.3.4+2.3.4.4+...+98.99.100.4
4S=1.2.3.4+2.3.4.(5-1)+...+98.99.100.(101-97)
4S=1.2.3.4+(2.3.4.5-1.2.3.4)+...+(98.99.100.101-97.98.99.100)
4S=(1.2.3.4+2.3.4.5+...98.99.100,101)-(1.2.3.4+2.3.4.5+...+97.98.99.100)
4S=98.99.100.101=97990200
S=24497550
e)\(S=1^2+2^2+3^2+...+99^2+100^2\)
\(S=1.\left(2-1\right)+2.\left(3-1\right)+3.\left(4-1\right)+...+99.\left(100-1\right)+100.\left(101-1\right)\)
\(S=\left(1.2-1\right)+\left(2.3-2\right)+\left(3.4-3\right)+...+\left(99.100-99\right)+\left(100.101-100\right)\)
\(S=\left(1.2+2.3+...+99.100+100.101\right)-\left(1+2+3+...+99+100\right)\)
Dựa vào kết quả câu a và c ta được:
S=333300-5050=328250
1) Tìm GTNN của A=(x-3)^2+|y+1|-3
2) Tính S=1.2.3+2.3.4+3.4.5+...+97.98.99
3) CMR:A=a^5-4 chia hết cho 30
Bài 1:
Ta thấy : \(\left\{\begin{matrix}\left(x-3\right)^2\ge0\\\left|y+1\right|\ge0\end{matrix}\right.\)
\(\Rightarrow\left(x-3\right)^2+\left|y+1\right|\ge0\)
\(\Rightarrow\left(x-3\right)^2+\left|y+1\right|-3\ge-3\)
\(\Rightarrow A\ge-3\)
Dấu "=" xảy ra khi \(\left\{\begin{matrix}\left(x-3\right)^2=0\\\left|y+1\right|=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x-3=0\\y+1=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x=3\\y=-1\end{matrix}\right.\)
Vậy \(Min_A=-3\) khi \(\left\{\begin{matrix}x=3\\y=-1\end{matrix}\right.\)
Bài 2:
\(S=1\cdot2\cdot3+2\cdot3\cdot4+...+97\cdot98\cdot99\)
\(4S=4\left(1\cdot2\cdot3+2\cdot3\cdot4+...+97\cdot98\cdot99\right)\)
\(4S=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot\left(5-1\right)+...+97\cdot98\cdot99\left(100-96\right)\)
\(4S=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4+...+97\cdot98\cdot99\cdot100-96\cdot97\cdot98\cdot99\)
\(4S=97\cdot98\cdot99\cdot100\Rightarrow S=\frac{97\cdot98\cdot99\cdot100}{4}=23527350\)
Tính
S=1+2-3-4+5+6-7-8+9+10-11-12+........+97+98-99-100
A=2100-299+298-297+......+22-2
bài 2 : s = 4 . 5 + 5.6 + 6.7+...+ 100.101
bài 3 : s= 1.2.3 + 2.3.4+ 3.4.5+...+ 98 . 99 .100
bài 4 : tính tổng sau: 1/5 + 1/25 + ... + 1/5 mu 100
Bài 1:
$A=1.2+2.3+3.4+...+201.202$
$3A=1.2.3+2.3(4-1)+3.4(5-2)+....+201.202(203-200)$
$=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+....+201.202.203-200.201.202$
$=(1.2.3+2.3.4+3.4.5+...+201.202.203)-(1.2.3+2.3.4+....+200.201.202)$
$=201.202.203$
$\Rightarrow A=\frac{201.202.203}{3}=2747402$
Bài 2:
$S=4.5+5.6+6.7+....+100.101$
$3S=4.5(6-3)+5.6.(7-4)+6.7.(8-5)+....+100.101(102-99)$
$=4.5.6-3.4.5+5.6.7-4.5.6+6.7.8-5.6.7+....+100.101.102-99.100.101$
$=(4.5.6+5.6.7+6.7.8+...+100.101.102)-(3.4.5+4.5.6+5.6.7+...+99.100.101)$
$=100.101.102-3.4.5$
$\Rightarrow S=\frac{100.101.102-3.4.5}{3}=343380$
Bài 3:
$S=1.2.3+2.3.4+3.4.5+...+98.99.100$
$4S=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+...+98.99.100(101-97)$
$=(1.2.3.4+2.3.4.5+3.4.5.6+...+98.99.100.101)-(0.1.2.3+1.2.3.4+2.3.4.5+...+97.98.99.100)$
$=98.99.100.101$
$\Rightarrow S=\frac{98.99.100.101}{4}$
Tính nhanh:
S=(2+4+6+8+.....+98+100)-(1+3+5+7+.......+97+99)
\(S=\left(2+4+...+100\right)-\left(1+3+5+...+99\right)\)
\(S=2+4+6+...+100-1-3-5-...-99\)
\(S=\left(2-1\right)+\left(4-3\right)+...+\left(100-99\right)\)
\(S=1+1+1+...+1\)
50 số hạng
\(S=5.1=5\)
Cái cuối cho mình sửa lại thành S = 50.1 = 50 nha
S= ( 2-1)+ (4-3) + (6-5)+....+ (100-99)
= 1+1+1+...+1 ( 50 chữ số 1)
=50.1 = 50
Tính nhanh:
S = 1 - 2 + 3 - 4 + 5 - 6 + ... + 199 - 200
S = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + ... + 97 + 98 - 99 - 100 + 101
Ai giải nhanh nhất mk hứa sẽ tick cho!
S=(1-2)+(3-4)+(5-6)+...+(199-200)
S=(-1)+(-1)+...+(-1)
S=(-1).100=-100
S=1+(2-3)+(-4+5)+...+(98-99)+(-100+101)
S=1+(-1)+1+..+(-1)+1
S=1+25.(-1)+25.1
S=1+(-25)+25
S=1+0
=1
S= 1+(1-3)+3+(1-5)+5+(1-7)+........+199+(1-199)=200