Tinh:
1/50 - 1/50 x 49 - 1/49x48-............-1/3x2 - 1/2x1
(1\(^2\) -1000) x ( 2\(^2\)x1000)........... ( 101\(^2\)-1000)
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a) A = 2 + 4 + 6 + 8 + ... + 1000
Ta có : A = 2 + 4 + 6 + 8 + ... + 1000 ( có 500 số )
= (1000 + 2) . 500 : 2 = 250500
c) \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}+\frac{2}{99.101}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}+\frac{1}{99}-\frac{1}{101}\)
\(=1-\frac{1}{101}=\frac{100}{101}\)
Ta có:
\(A=\left(1000-1^3\right).\left(1000-2^3\right).........\left(1000-50^3\right)\)
\(A=\left(1000-1^3\right).\left(1000-2^3\right).......\left(1000-10^3\right)........\left(1000-50^3\right)\)
\(A=0.\left(1000-1^3\right).\left(1000-2^3\right)....\left(1000-9^3\right).\left(1000-11^3\right).....\left(1000-50^3\right)\)
A = 0
1=ĐS=1
2=ĐS=2000
3=ĐS=0
4=ĐS=7036
K MÌNH NHA
Bài 1: Tính nhanh
A, 13 x 126 + 37 x 126 - 49 x 126
= 126 x ( 13 + 49 - 49 )
= 126 x 1
= 126
B, ( 1 + 2 + 4 + 8+.....+ 512 ) x ( 101 x 102 - 101 x 101 - 50 - 51 )
= ( 1 + 2 + 4 + 8+.....+ 512 ) x ( 101 x ( 102 - 101 - 1))
= ( 1 + 2 + 4 + 8+.....+ 512 ) x ( 101 x 0)
= ( 1 + 2 + 4 + 8+.....+ 512 ) x 0
= 0
(1000 - 13) x (1000 - 23) x (1000 - 33) x ... x (1000 - 103) x ... x (1000 - 503)
= (1000 - 13) x (1000 - 23) x (1000 - 33) x ... x (1000 - 1000) x ... x (1000 - 503)
= (1000 - 13) x (1000 - 23) x (1000 - 33) x ... x 0 x ... x (1000 - 503)
= 0
(1000 - 13)(1000 - 23)(1000 - 33)........(1000 - 503)
= (1000 - 13)(1000 - 23)(1000 - 33)....(1000 - 103)....(1000 - 503)
= (1000 - 13)(1000 - 23)(1000 - 33).....(1000 - 1000)...(1000 - 503)
= (1000 - 13)(1000 - 23)(1000 - 33).....0...(1000 - 503)
= 0
a: \(=\dfrac{1}{50}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)\)
\(=\dfrac{1}{5}-\dfrac{49}{50}=\dfrac{-48}{50}=-\dfrac{24}{25}\)
501−(1−21+21−31+...+491−501)
=15−4950=−4850=−2425=51−5049=50−48=−2524