S₁ = 10 + 12 + 14 + ... + 2010: Có 1001 số hạng

=> (10 + 2010) . 1001 : 2 = 1011010

S₂ = 21 + 23 + 25 + ... + 1001: Có 491 số hạng

=> (21 + 1001) . 491 : 2 = 250901

S₃ = 1 + 4 + 7 + ... + 79: Có 27 số hạng

=> (1 + 79) . 27 : 2 = 1080

S₄ = 15 + 17 + 19 + 21 + ... + 151 + 153 + 155: Có 71 số hạng.

=> (155 + 15) . 71 : 2 = 6035

s2=4250901

s1=1011010

s3=1018

s4=6035

a) số số hạng là 999

tổng là \(\dfrac{\left(1+999\right).999}{2}=49950\)

b)sô số hạng là \(\dfrac{2010-10}{2}+1=1001\)

tổng là \(\dfrac{\left(10+2010\right).1001}{2}=1011010\)

c) số số hạng là \(\dfrac{79-1}{3}=26\)

tổng là \(\dfrac{\left(79+1\right).26}{2}=1040\)

2 . tìm x :

a ) 5^2x = 625

 5^2x = 5⁴

=> 2 . x = 4

x = 4 : 2

x = 2

b ) 9^x-1 = 9

9^x-1 = 9¹

=> x - 1 = 1

x = 1 + 1

x = 2

c ) 2^x : 2⁵ = 1

2^x-5 = 1

=> x = 5 , vì 2^5-5 = 2⁰ = 1

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) \(S_7=15+25+35+45+......+115\)

\(\Rightarrow S_7=\dfrac{\left(115+15\right).\left[\left(115-15\right):10+1\right]}{2}\)

\(\Rightarrow S_7=\dfrac{130.\left(100:10+1\right)}{2}\)

\(\Rightarrow S_7=\dfrac{130.\left(10+1\right)}{2}\)

\(\Rightarrow S_7=\dfrac{130.11}{2}\)

\(\Rightarrow S_7=\dfrac{1430}{2}\)

\(\Rightarrow S_7=715\)

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

255510 đó