1/1+2+1/1+2+3+1/1+2+3+4+............................+1/1+2+3+..........................+99+1/50
Những câu hỏi liên quan
tinh 1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+4+...+99)+1/50
sao bn ko tra trên mạng ấy
1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+1/(1+2+3+4+5)...+1/(1+2+3+4+5...+99)+1/50 là:
Đặt \(S=\frac{1}{1+2}+\frac{1}{1+2+3}+....+\frac{1}{1+2+.....+99}+\frac{1}{50}\)
Đặt E = \(\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+....+99}\)
\(E=\frac{1}{2.3:2}+\frac{1}{3.4:2}+....+\frac{1}{99.100:2}\)
\(\frac{1}{2}E=\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)
E = 49/100 : 1/2 = 49/50
Vậy \(S=\frac{49}{50}+\frac{1}{50}=\frac{50}{50}=1\)
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Bài 4: Tính tổng 1) 1 + (-2) + 3 + (-4) + . . . + 19 + (-20) 2) 1 – 2 + 3 – 4 + . . . + 99 – 100 3) 2 – 4 + 6 – 8 + . . . + 48 – 50 4) – 1 + 3 – 5 + 7 - . . . . + 97 – 99 5) 1 + 2 – 3 – 4 + ... + 97 + 98 – 99 - 100
1. 1 + ( -2) +3 +(-4) + .........+ 19 + (-20)
= -1 + ( -1) +....+(-1)
= -1. 10
= -10
2. 1 – 2 + 3 – 4 + . . . + 99 – 100
= ( -1) + (-1) +....+(-1)
= -1. 50
= -50
3. 2 – 4 + 6 – 8 + . . . + 48 – 50
= (-2) + (-2) +....+ (-2)
= -2. 12 + 26
= -24 + 26
= 2
4. – 1 + 3 – 5 + 7 - . . . . + 97 – 99
= 2 + 2 +......+2
= 2.25
= 50
5. 1 + 2 – 3 – 4 + ... + 97 + 98 – 99 - 100
= (1+2-3-4) +......+ ( 97+98-99 -100)
= -4 . (-4).....(-4)
= -4. 25
= -100
\((^1/1+2) + (^1/1+2+3) + (^1/1+2+3+4) +...+(^1/1+2+3+4+...+99) + (^1/50)\)
= 2*(1/1 - 1/2 + 1/2 - ...... - 1/100) + 1/50
= 2*(1 - 1/100) + 1/50
= 2*99/100 + 1/50
= 99/50 + 1/50 = 2
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= 2*(1/1 - 1/2 + 1/2 - ...... - 1/100) + 1/50
= 2*(1 - 1/100) + 1/50
= 2*99/100 + 1/50
= 99/50 + 1/50 = 2
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1/1+2 + 1/1+2+3 + 1/1+2+3+4 + ... + 1/1+2+3+4+...+99 +1/50 ( cach giai )
1/1+(-2)+3+(-4)+...+19+(-20)
2/1-2+3-4+...+99-100
3/2-4+6-8+...+48-50
4/-1+3-5+7-...+97-99
5/1+2-3-4+...+97+98-99-100
1: =(1-2)+(3-4)+...+(19-20)
=(-1)+(-1)+...+(-1)
=-10
2: =(1-2)+(3-4)+...+(99-100)
=(-1)+(-1)+...+(-1)
=-50
4: =(-1+3)+(-5+7)+...+(-97+99)
=2+2+...+2
=2x50=100
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Tính:
M=(1-1/2^2).(1-1/3^2).(1-1/4^2)...(1-1/49^2).(1-1/50^2)
N=(3/2-2/2^2).(4/3-2/3^2).(5/4-2/4^2)...(100/99-2/99^2).(101/100-2/100^2)
??????????????????????????????????????????
1. Tính tổng:
1/ 1 + (-2) + 3 + (-4) +...+ 19 + (-20)
2/ 1 - 2 + 3 - 4 +..+ 99 - 100
3/ 2 - 4 + 6 - 8 +...+ 48 - 50
4/ -1 + 3 - 5 + 7 -...+ 97 - 99
5/ 1 + 2 - 3 - 4 +...+ 97 + 98 - 99 - 100
Giá trị biểu thức 1/1+2 + 1/1+2+3 + 1/1+2+3+4 +...+ 1/1+2+3+...+99 + 1/50 là
A = \(\dfrac{1}{1+2}\) + \(\dfrac{1}{1+2+3}\) + ... + \(\dfrac{1}{1+2+3+...+99}\) + \(\dfrac{1}{50}\)
A = \(\dfrac{1}{\left(2+1\right).2:2}\) + \(\dfrac{1}{\left(3+1\right).3:2}\) + ... + \(\dfrac{1}{\left(99+1\right).99:2}\) + \(\dfrac{1}{50}\)
A = \(\dfrac{2}{2.3}\) + \(\dfrac{2}{3.4}\) + \(\dfrac{2}{4.5}\) + ... + \(\dfrac{2}{99.100}\) + \(\dfrac{1}{50}\)
A = 2.(\(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\) + ... + \(\dfrac{1}{99.100}\)) + \(\dfrac{1}{50}\)
A = 2.(\(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}-\dfrac{1}{5}\)+ \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\) + ... + \(\dfrac{1}{99}\) - \(\dfrac{1}{100}\)) + \(\dfrac{1}{50}\)
A = 2.(\(\dfrac{1}{2}\) - \(\dfrac{1}{100}\)) + \(\dfrac{1}{50}\)
A = 2.(\(\dfrac{50}{100}\) - \(\dfrac{1}{100}\)) + \(\dfrac{1}{50}\)
A = 2.\(\dfrac{49}{100}\) + \(\dfrac{1}{50}\)
A = \(\dfrac{49}{50}\) + \(\dfrac{1}{50}\)
A = 1
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