S1=1+2+3+....+999
S2=10+12+14+......+2010
S3=21+23+25+.....+1001
S7=15+25+35+.....+115
S5=1+4+7+.....+79
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1)
S1=(1+999)+(2+998)+...+(501+499)+500
S1=1000.(999-1)+500
S1=998 000 + 500
S1=998 500
:/ câu 1 quá ez mik bik làm rồi còn các câu sau nó thì mik chịu
a) \(S_1=1+2+3+4+......+999\)
\(\Rightarrow S_1=\dfrac{\left(999+1\right).\left[\left(999-1\right):1+1\right]}{2}\)
\(\Rightarrow S_1=\dfrac{1000.\left(998+1\right)}{2}\)
\(\Rightarrow S_1=\dfrac{1000.999}{2}\)
\(\Rightarrow S_1=\dfrac{999000}{2}\)
\(\Rightarrow S_1=499500\)
b) \(S_2=10+12+14+......+2010\)
\(\Rightarrow S_2=\dfrac{\left(2010+10\right).\left[\left(2010-10\right):2+1\right]}{2}\)
\(\Rightarrow S_2=\dfrac{2020.\left(2000:2+1\right)}{2}\)
\(\Rightarrow S_2=\dfrac{2020.\left(1000+1\right)}{2}\)
\(\Rightarrow S_2=\dfrac{2020.1001}{2}\)
\(\Rightarrow S_2=\dfrac{2022020}{2}\)
\(\Rightarrow S_2=1011010\)
c) \(S_3=21+23+25+.......1001\)
\(\Rightarrow S_3=\dfrac{\left(1001+21\right).\left[\left(1001-21\right):2+1\right]}{2}\)
\(\Rightarrow S_3=\dfrac{1022.\left(980:2+1\right)}{2}\)
\(\Rightarrow S_3=\dfrac{1022.\left(490+1\right)}{2}\)
\(\Rightarrow S_3=\dfrac{1022.491}{2}\)
\(\Rightarrow S_3=\dfrac{501802}{2}\)
\(\Rightarrow S_3=250901\)
d) \(S_5=1+4+7+......+79\)
\(\Rightarrow S_5=\dfrac{\left(79+1\right).\left[\left(79-1\right):3+1\right]}{2}\)
\(\Rightarrow S_5=\dfrac{80.\left(78:3+1\right)}{2}\)
\(\Rightarrow S_5=\dfrac{80.\left(26+1\right)}{2}\)
\(\Rightarrow S_5=\dfrac{80.27}{2}\)
\(\Rightarrow S_5=\dfrac{2160}{2}\)
\(\Rightarrow S_5=1080\)
e) \(S_7=15+25+35+45+......+115\)
\(\Rightarrow S_7=\dfrac{\left(115+15\right).\left[\left(115-15\right):10+1\right]}{2}\)
\(\Rightarrow S_7=\dfrac{130.\left(100:10+1\right)}{2}\)
\(\Rightarrow S_7=\dfrac{130.\left(10+1\right)}{2}\)
\(\Rightarrow S_7=\dfrac{130.11}{2}\)
\(\Rightarrow S_7=\dfrac{1430}{2}\)
\(\Rightarrow S_7=715\)
2 . tìm x :
a ) 52x = 625
52x = 54
=> 2 . x = 4
x = 4 : 2
x = 2
b ) 9x-1 = 9
9x-1 = 91
=> x - 1 = 1
x = 1 + 1
x = 2
c ) 2x : 25 = 1
2x-5 = 1
=> x = 5 , vì 25-5 = 20 = 1
Đặt cột s+s theo từng cặp số hạng (số đầu-số đuôi) nhé:
s = 1 + 2 + 3 +...+ 999
+
s = 999 + 998 + 997 +...+ 1
__________________________
2s=1000+1000+1000+...+1000
2s=1000.999 (từ 1 đến 999 <=> có 999 số hạng)
=> s= 500.999= 499500
S1= 1+2+3...+999
S1= (999-1) :1 +1= 999
S1= (999+1) x999 :2=499500
S1= 499500
S2= ( 1010 -10) : 2 +1= 501
S2= (1010+ 10) x 501:2= 255510