\(Q=\left(-1\right)+\left(-3\right)+\left(-5\right)+.....+\left(-99\right)\)
Những câu hỏi liên quan
\(H=\frac{\left(1+97\right)\left(1+\frac{97}{2}\right)\left(1+\frac{97}{3}\right)\left(1+\frac{97}{4}\right)+...+\left(1+\frac{97}{99}\right)}{\left(1+99\right)\left(1+\frac{99}{2}\right)\left(1+\frac{99}{3}\right)\left(1+\frac{99}{4}\right)+...+\left(1+\frac{99}{97}\right)}\)
tinh nhanh:\(1+\left(-3\right)+5+\left(-7\right)+9+\left(11\right)+...+\left(-99\right)\)99)
Tách đôi ra ÁP CÔNG THÚC TỔNG VÀO:
a=1+5+..+97
B=-3+-7+..-99=-(3+...+99)
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c)\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+\left(x+4\right)+\left(x+5\right)=90\)
d)\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+.....+\left(x+99\right)+\left(x+100\right)+=20150\)
c) (x+1) + (x+2) + ... + (x+5) = 90
=> 5x + ( 1 + 2 + ... + 5 ) = 90
5x + 15 = 90
5x = 90 - 15
5x = 75
x = 75 : 5
x = 15
d) (x+1) + (x+2) + .... + (x+100) = 20150
=> 100x + ( 1+2+...+100 ) = 20150
100x + 5050 = 20150
100x = 20150 - 5050
100x = 15100
x = 15100 : 100
x = 151
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Ta có : (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) = 90
<=> x + x + x+ x + x + (1 + 2 + 3 + 4 + 5) = 90
<=> 5x + 15 = 90
=> 5x = 75
=> x = 15
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c) \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+\left(x+4\right)+\left(x+5\right)=90\)
\(\Leftrightarrow x+1+x+2+x+3+x+4+x+5=90\)
\(\Leftrightarrow5x+\left(1+2+3+4+5\right)=90\)
\(\Leftrightarrow5x+15=90\)
\(\Leftrightarrow5x=75\)
\(\Leftrightarrow x=15\)
d) \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+......+\left(x+99\right)+\left(x+100\right)=20150\)
\(\Leftrightarrow x+1+x+2+x+3+......+x+99+x+100=20150\)
\(\Leftrightarrow100x+\left(1+2+3+.....+99+100\right)=20150\)
\(\Leftrightarrow100x+5050=20150\)
\(\Leftrightarrow100x=15100\)
\(\Leftrightarrow x=151\)
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25 tháng 2 2023 lúc 19:22
\(99^{99}\)-\(\left\{1,\left(3\right)-\left[5\times2^3-\left(-7^2\right)+\dfrac{1}{3}+99^9\times\left(27^4-81^3-99^{90}\right)\right]\right\}\)
Giai hệ PT bằng phương pháp cộng
a.left{{}begin{matrix}5.left(x+2yright)-3.left(x-yright)99x-3y7x-4y-17end{matrix}right.
b.left{{}begin{matrix}3.left(y-5right)+2left(x-3right)07.left(x-4right)+3left(x+y-1right)14end{matrix}right.
c.left{{}begin{matrix}2.left(x+1right)-5left(y+1right)83.left(x+1right)-2.left(y+1right)1end{matrix}right.
d.left{{}begin{matrix}2.left(3y+1right)-4left(x-1right)55.left(3y+1right)-8left(x-1right)9end{matrix}right.
Đọc tiếp
Giai hệ PT bằng phương pháp cộng
a.\(\left\{{}\begin{matrix}5.\left(x+2y\right)-3.\left(x-y\right)=99\\x-3y=7x-4y-17\end{matrix}\right.\)
b.\(\left\{{}\begin{matrix}3.\left(y-5\right)+2\left(x-3\right)=0\\7.\left(x-4\right)+3\left(x+y-1\right)=14\end{matrix}\right.\)
c.\(\left\{{}\begin{matrix}2.\left(x+1\right)-5\left(y+1\right)=8\\3.\left(x+1\right)-2.\left(y+1\right)=1\end{matrix}\right.\)
d.\(\left\{{}\begin{matrix}2.\left(3y+1\right)-4\left(x-1\right)=5\\5.\left(3y+1\right)-8\left(x-1\right)=9\end{matrix}\right.\)
d: =>6y+2-4x+4=5 và 15y+5-8x+8=9
=>-4x+6y=-1 và -8x+15y=-4
=>x=-3/4; y=-2/3
c: \(\Leftrightarrow\left\{{}\begin{matrix}x+1=-1\\y+1=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=-3\end{matrix}\right.\)
b: \(\Leftrightarrow\left\{{}\begin{matrix}3y-15+2x-6=0\\7x-28+3y+3y-3=14\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+3y=21\\7x+6y=45\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=\dfrac{19}{3}\end{matrix}\right.\)
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a)\(\left(1\frac{1}{3}\right)\left(1\frac{1}{8}\right)\left(1\frac{1}{15}\right)...\left(1\frac{1}{99}\right)\)
b)\(\left(1+\frac{1}{3}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{15}\right)\left(1+\frac{1}{24}\right)\left(1+\frac{1}{99}\right)\)
Tính tổng sau:
\(1+\left(-2\right)+\left(3\right)+\left(-4\right)+5+.....+\left(-98\right)+99\)
\(1+\left(-2\right)+3+\left(-4\right)+5+...+\left(-98\right)+99\)
\(=\left(1+3+5+...+99\right)+\left[\left(-2\right)+\left(-4\right)+...+\left(-98\right)\right]\)
\(=\frac{100.50}{2}+\frac{-100.49}{2}\)
\(=2500+\left(-2450\right)\)
\(=50\)
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\(1+\left(-2\right)+3+\left(-4\right)+...+\left(-98\right)+99\)
\(=\left(1+3+...+99\right)+\left[\left(-2\right)+\left(-4\right)+...+\left(-98\right)\right]\)
\(=\frac{\left(99+1\right).50}{2}+\frac{\left[\left(-98\right)+\left(-2\right)\right].50}{2}\)
\(=2550+\left(-2450\right)=50\)
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Tính
\(\frac{3}{\left(x+2\right)\left(x+3\right)}\)+\(\frac{3}{\left(x+3\right)\left(x+5\right)}\)+ \(\frac{3}{\left(x+5\right)\left(x+7\right)}\)+ ... + \(\frac{3}{\left(x+99\right)\left(x+101\right)}\)
\(\frac{3}{\left(x+1\right)\left(x+3\right)}=\frac{3}{2}.\frac{\left(x+3\right)-\left(x+1\right)}{\left(x+3\right)\left(x+1\right)}=\frac{3}{2}\left(\frac{1}{x+1}-\frac{1}{x+3}\right)\)
Tương tự:
\(\frac{3}{\left(x+3\right)\left(x+5\right)}=\frac{3}{2}.\left(\frac{1}{x+3}-\frac{1}{x+5}\right)\)
\(\frac{3}{\left(x+5\right)\left(x+7\right)}=\frac{3}{2}\left(\frac{1}{x+5}-\frac{1}{x+7}\right)\)
.....
\(\frac{3}{\left(x+99\right)\left(x+101\right)}=\frac{3}{2}\left(\frac{1}{x+99}-\frac{1}{101}\right)\)
Cộng các vế lại ta có:
\(\frac{3}{\left(x+1\right)\left(x+3\right)}+\)\(\frac{3}{\left(x+3\right)\left(x+5\right)}+\)\(\frac{3}{\left(x+5\right)\left(x+7\right)}+\)...\(+\frac{3}{\left(x+99\right)\left(x+101\right)}\)
=\(\frac{3}{2}\left(\frac{1}{x+1}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+5}+\frac{1}{x+5}-\frac{1}{x+7}+...+\frac{1}{x+99}-\frac{1}{x+101}\right)\)
=\(\frac{3}{2}\left(\frac{1}{x+1}-\frac{1}{x+101}\right)\)
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\(\left(-1\right).\left(-1\right)^2.\left(-1\right)^3.\left(-1\right)^4....\left(-1\right)^{99}\)
ta thấy tất cả các biểu thức ở trên đều chỉ có kết quả là -1 hoặc 1
ta có t/c khi số mũ của một số nguyên âm là số lẻ thì nó sẽ là số âm và ngược lại khi số mũ đó chẳn thì nó là nguyên dương
vì thế (_1)99 =-1
(-1).(-1)2...(-1)98.-1=-1
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