CMR:1/10^2+1/15^2+...+1/500^2<1/15
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chung minh rang 1/10^2+1/15^2+1/20^2+...+1/500^2<1/15
CMR1/10^2+1/15^2+...+1/500^2<1/15
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500-{5[409-(2^3.3-21)^2]+10^3}:15
{[(3^2+1).10-(8:2+6)]:2}+55-10(10:5)^3
1/1 x 10 + 1/2 x 15 + 1/3 x 20+...........................................+1/98 x 495 + 1/99 x 500
1-3/2×10 - 3/4×15 - 3/8×15 -...-3/198×500
(CMR:1-1/2+1/3-1/4+...-1/498+1/499-1/500=1/247+1/248+1/249+...+1/500).
tính giá trị của tổng sau :
1/1 x 10 + 1/2 x 15 + 1/3 x 20 + ... + 1/89 x 495 + 1/ 99 x 500
\(\frac{1}{1\times10}+\frac{1}{2\times15}+\frac{1}{3\times20}+...+\frac{1}{98\times495}+\frac{1}{99\times500}\)
\(=\frac{1}{1\times2\times5}+\frac{1}{2\times3\times5}+\frac{1}{3\times4\times5}+...+\frac{1}{98\times99\times5}+\frac{1}{99\times100\times5}\)
\(=\frac{1}{5}\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{98\times99}+\frac{1}{99\times100}\right)\)
\(=\frac{1}{5}\times\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)
\(=\frac{1}{5}\times\left(1-\frac{1}{100}\right)=\frac{1}{5}\times\frac{99}{100}=\frac{99}{500}\)
\(\frac{1}{1\times10}+\frac{1}{2\times15}+\frac{1}{3\times20}+...+\frac{1}{98\times495}+\frac{1}{99\times500}\)
\(=\frac{1}{1\times2\times5}+\frac{1}{2\times3\times5}+\frac{1}{3\times4\times5}+...+\frac{1}{98\times90\times5}+\frac{1}{90\times100\times5}\)
\(=\frac{1}{5}\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{98\times99}+\frac{1}{99\times100}\right)\)
\(=\frac{1}{5}\times\left(\frac{2-1}{1\times2}+\frac{3-2}{2\times3}+...+\frac{99-98}{98\times99}+\frac{100-99}{99\times100}\right)\)
\(=\frac{1}{5}\times\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)
\(=\frac{1}{5}\times\left(1-\frac{1}{100}\right)=\frac{99}{500}\)
cảm ơn bạn Xyz và bạn Đoàn Đức Hà nhìu (^-^) thank you !!!!!!!!!!!!!!!!!
BT 1:tính A) 10 mũ hai -[60:(5 mũ 6 : 5 mũ 4 -3.5 )] B) 160 :{177 [ 3 mũ 2 .5-( 14 + 2 mũ 11 : 2 mũ 8)]} C) 500 - { 5 x [ 409 -( 2 mũ 2 .3 -21) mũ 2 ] + 10 mũ 3 } : 15 D) 100 + 98 +96+......2-97=95...-1
1 tính nhanh
a 1/1*10+1/2*15+1/3*20+...+1/98*495+1/99*500
b 11/12 +19/20+29/30 +41/42+55/56