thuc hien phep cac phep tinh sau:
a, (1-1/2).(1-1/3).(1-1/4)...(1-1/100)
b, (1+1/1.3).(1+1/2.4).(1+1/3.5)...(1+1/99.101)
1:" thuc hien phep tinh : (-1)+2-3+4-....-99+100
1/4 - 1/3+ 5/12 Thuc hien cac phep tinh (tinh hop li neu co the)
\(\dfrac{1}{4}-\dfrac{1}{3}+\dfrac{5}{12}\\ =\dfrac{3}{12}-\dfrac{4}{12}+\dfrac{5}{12}\\ =\dfrac{3-4+5}{12}\\ =\dfrac{4}{12}\\ =\dfrac{1}{3}\)
Tính
A=(1-1/2).(1-1/3).(1-1/4).....(1-1/100)
B= (1+1/1.3).(1+1/2.4).(1+1/3.5).....(1+1/99.101)
thuc hien phep tinh sau 1 cach hop li B=(-1).(-1)^2 . (-1)^3........ (-1)^2013
\(B=\left(-1\right)\left(-1\right)^2\left(-1\right)^3...\left(-1\right)^{2013}\)
\(B=\left(-1\right)^{1+2+3+...+2013}\)
Tính tổng dãy số 1+2+3+..+2013:
+) Số các số hạng: (2013-1):1+1=2013
+) Tổng: (1+2013).2013:2=2027091.
\(B=\left(-1\right)^{2027091}=-1\)
đơn giản thôi
vì -1 mũ chắn sẽ = 1, mũ lẻ sẽ = -1
mà - 1 x -1 = 1, nên (-1)^2 x.........x (-1)^2013 sẽ được kết quả = 1
B=(-1) x 1 = -1
làm theo cách của Trần Thiên kim cũng đúng và có thể sẽ dễ hiểu hơn
thuc hien phep tinh:
P=(1/2-1*1/3-1*1/4-1*...1/2017-1*1/2018-1)
thuc hien phep tinh :M=1+1/2(1+2)+1/3(1+2+3)+1/4(1+2+3+4)+...+1/16(1+2+3+...+16)
thuc hien phep tinh (1-1/(1+2)).(1-1/(1+2+3))...(1-1/(1+2+3+...+2006))
bai 1: Thuc hien phep tinh
a) 75/100 + 18/21 + 19/32 + 1/4 + 3/21 + 13/32
b) 22/5 + 51/9 + 11/4 + 3/5 + 1/3 + 1/4
1a
75/100+18/21+19/32+1/4+3/21+13/32
= 3/4 +6/7+19/32+1/4+1/7+13/32
= (3/4+1/4)+(19/32+13/32)+(6/7+1/7)
= 1+1+1=3
1b
22/5+51/9+11/4+3/5+1/3+1/4
=22/5+17/3+11/4+3/5+1/3+1/4
=(22/5+3/5)+(17/3+1/3)+(11/4+1/4)
=25/5+18/3+12/4
=5+6+3
=14
Thuc hien phep tinh
A, 3/7 + 1/2 - (-3)/70
B, 3/5 + -1/25 - 35/100
C, 5/12 - 3/-16 + 3/4
D, 5/15 + 4/-12 + 1/7 - 1/-6
a,3/7 +1/2-[-3]/70
=13/14 -[-3]/70
=65/70 -[-3]/70
=34/35
b,3/5+-1/25 -35/100
=14/25 - 35/100
=56 /100 -35/100
= 21/100
c ,5/12 -3/-16+3/4
=29/48 +3/4
= 29/48 +36/48
=65/48
d, 5/15 +4/-12 +1/7 -1/-6
= 1/3 +1/-3 +1/7-1/-6
=0+1/7-1/-6
= 13/42
A.\(\dfrac{3}{7}+\dfrac{1}{2}+\dfrac{\left(-3\right)}{70}\)
=\([\dfrac{30}{70}+\dfrac{\left(-3\right)}{70}]\)+\(\dfrac{1}{2}\)
= \(\dfrac{27}{70}+\dfrac{35}{70}\)
=\(\dfrac{62}{70}=\dfrac{31}{35}\)
B.\(\dfrac{3}{5}+\dfrac{-1}{25}-\dfrac{35}{100}\)
=\(\dfrac{60}{100}+\dfrac{-4}{100}-\dfrac{35}{100}\)
=\(\dfrac{60+\left(-4\right)-35}{100}\)
=\(\dfrac{21}{100}\)
C.\(\dfrac{5}{12}-\dfrac{3}{-16}+\dfrac{3}{4}\)
=\(\left(\dfrac{5}{12}+\dfrac{9}{12}\right)-\dfrac{-3}{16}\)
=\(\dfrac{7}{6}-\dfrac{-3}{16}\)
=\(\dfrac{56}{48}-\dfrac{-9}{48}\)=\(\dfrac{65}{48}\)
D.\(\dfrac{5}{15}+\dfrac{4}{-12}+\dfrac{1}{7}-\dfrac{1}{-6}\)
=\(\dfrac{1}{3}+\dfrac{1}{7}+(\dfrac{-2}{6}-\dfrac{-1}{6})\)
=\(\dfrac{1}{3}+\dfrac{1}{7}+\dfrac{-1}{6}\)
=\((\dfrac{1}{3}+\dfrac{-1}{6})+\dfrac{1}{7}\)
=\(\dfrac{1}{6}+\dfrac{1}{7}\)=\(\dfrac{13}{42}\)