Tính nhanh:3/2+7/6+13/12+21/20+...+133/132
Tính nhanh:3/2+7/6+13/12+21/20+...+133/132
3/2+7/6+13/12+21/20+...+133/132
=1+ 1/2 + 1+ 1/6 + 1+ 1/12 + 1+ 1/20+......+ 1+ 1/132
=(1+ 1 + 1+.....+ 1) + ( 1/2+ 1/6+1/12+ 1/20+....+ 1/132)
= 11+ ( 1/1×2+ 1/2×3+1/3×4+1/4×5+.....+1/11×12)
=11+ ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/11-1/12)
=11+(1-1/12)
= 11+11/12
=143/12
Tính nhanh tổng:
a, S=1 - 1/5 +7/12 -9/20 + 11/30 - 13/42 + 15/56 + 19/90 - 21/110 + 23/132
b, P=21 * (4/1*3 - 8/3*5 + 12/5*7 - 16/7*9 + ... + 36/17*19 - 40/19*21 ( dấu * là dấu nhân nhé)
Tính nhanh:3/2+7/6+13/12+21/20+31/30+43/42+57/56+73/72
Tính nhanh
A=111/110+91/90+73/72+…………+21/20+13/12+7/6+3/2
A = 1 + 1/110 + 1 + 1/90 + ... + 1 + 1 /2
A = 10 + 1/1.2+ 1 /2.3 + ... + 1/9.10 + 1/10.11
A = 10 + 1/1 - 1/2 + 1 /2 - 1/3 + ... + 1/9 - 1/10 + 1/10 - 1/11
A = 10 + 1/1 - 1/11
A = 10 + 10/11
A = 120/11
A = \(\frac{111}{110}+\frac{91}{90}+\frac{73}{72}+...+\frac{13}{12}+\frac{7}{6}+\frac{3}{2}\)
A = \(\left(\frac{1}{2}+1\right)+\left(\frac{1}{6}+1\right)+\left(\frac{1}{12}+1\right)+....+\left(\frac{1}{110}+1\right)\)
A = (1 + 1 + 1 +...+ 1) + \(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)\)
A = 10 + \(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)
A = \(10+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)\)
A = \(10+\left(1-\frac{1}{11}\right)\)
A = \(10+\frac{10}{11}\)
A = \(\frac{120}{11}\)
Tính tổng A= 1- 5/6 +7/12 - 9/20 + 11/30 - 13/42 + 15/56 - 17/72 + 19/90 - 21/110 + 23/132 - 25/156
Tính nhanh
a) 23 - 21 + 19 - 17 + 15 - 13 + 11 - 9 + 7 - 5 + 3 - 1;
b) 24 - 22 + 20 - 18 + 16 - 14 + 12 - 10 + 8 - 6 + 4 - 2
a. ( 23 - 21) + ( 19 - 17) + ( 15 - 13) + ( 11 - 9) + ( 7 - 5) + ( 3 - 1)
= 2 + 2 + 2 + 2 + 2 + 2
= 2 x 6
= 12
b. ( 24 - 22 ) + ( 20 - 18 ) + ( 16 - 14 ) + ( 12 - 10) + ( 8 - 6 ) + ( 4 - 2)
= 2 + 2 + 2 + 2 + 2 + 2
= 2 x 6
= 12
+\(\dfrac{1}{3^{100}}\) với
A = \(\dfrac{1}{3}\) + \(\dfrac{1}{3^2}\) + \(\dfrac{1}{3^3}\)+...+ \(\dfrac{1}{3^{99}}\) + \(\dfrac{1}{3^{100}}\)
3A = 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{3^2}\) + \(\dfrac{1}{3^3}\)+...+ \(\dfrac{1}{3^{99}}\)
3A - A = 1 - \(\dfrac{1}{3^{100}}\)
2A = 1 - \(\dfrac{1}{3^{100}}\)
A = \(\dfrac{1}{2}\) - \(\dfrac{1}{2.3^{100}}\) < \(\dfrac{1}{2}\)
Bài 2: Tính
1) -25 + 13
2) -17 + 28
3) - 37 + 65;
4) (-4) . 51
5) 12 – 25
6) (-13) + (-30)
7) (-12) – 24
8) (-15) . (-11) + 123
9) (-150) : 3 + (-20).(-5)
10) (72 + 22 – 65) – (67 + 12 – 75)
Bài 3: Tính nhanh
1) - 138 + 57 + (-62) + 43
2) 12 – 17 + 38 – 43
3) 100 + ( -520) + 1140 + ( -620);
4) 15 . (-32) + 15 . (-42) + 15 . (-26)
Bài 4: Tìm x biết:
1) x + 49 = 31 2) 15 – x = 12 – (-19)
3) 2x – 20 = -14; 4) x + 79 = - 24
5) 36 – x = 12 – (-39) 6) x – 29 = -14;
7) x + 36 = 15 – ( -19) 8) 5x – 15 = - 225
Bài 5: Tìm tổng các số nguyên x ,biết:
1) 2)
3)
4)
1, Thực hiện phép tính ( tính hợp lý nếu có thể) A, -1/12+4/3 B,(-4/14-3/15)-(1/5-20/35- -1)7 C, 3/5+ -5/20+30/75+ -7/4 D, 5/6. -12/13 + 7/13 E, 2/-9 - 5/-36 - 1/4 F, 2/23 +-5/12+7/18+21/23+ -7/12
c) Ta có: \(\dfrac{3}{5}+\dfrac{-5}{20}+\dfrac{30}{75}+\dfrac{-7}{4}\)
\(=\dfrac{3}{5}+\dfrac{2}{5}+\dfrac{-1}{4}+\dfrac{-7}{4}\)
\(=1-2=-1\)
Giải:
a)-1/12+4/3=-1/12+16/12=15/12=5/4
b)(-4/14-3/15)-(1/5-20/35-(-1)).7
=-17/35-22/35.7
=-17/35-22/5
=-171/35
c)3/5+-5/20+30/75+-7/4
=3/5+-1/4+2/5+-7/4
=(3/5+2/5)+(-1/4+-7/4)
=1+-2
=-1
d)5/6.-12/14+7/13
=-5/7+7/13
=-16/91
e)2/-9-5/-36-1/4
=-1/12-1/4
=-1/3
f)2/23+-5/12+7/18+21/23+-7/12
=(2/23+21/23)+(-5/12+-7/12)+7/18
=1+-1+7/18
=7/18