\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{50}}\)
\(\Rightarrow3A=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{49}}\)
\(\Rightarrow3A-A=\left(1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{49}}\right)-\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{50}}\right)\)
\(\Rightarrow2A=1-\dfrac{1}{3^{50}}\)
\(\Rightarrow A=\dfrac{1-\dfrac{1}{3^{50}}}{2}\)
1, A=1/1 mu 2 + 1/2 mu 2+ 1/3 mũ 2 +1/4 mu 2+...........+1/50 mũ 2 . Chứng minh A<2
2, Tính tổng : S= 3+3/2+3/2 mu 2+...............+ 3/2 mũ 9
Bài 1 : Tính :
a, D = 1^2 + 3^2 + 5^2 + ..... + 97^2 + 99^2
b. E = 1^2 - 2^2 + 3^2 - 4^2 + ... + 99^2 - 100^2
c,A = 1^2 + 2^2 + .... + 200^2
d, B = 1^2 + 3^2 + 5^2 + ... 199^2
e, C = 2^2 + 4^2 + 6^2 + ... + 200^2
g, H = 1^2 - 2^2 + 3^2 - 4^2 + ... + 199^2 - 200^2
k, M = 1^3 + 2^3 + 3^3 + ..... + 50^31) C/m: 1/26+1/27+1/28+....+1/50 < 1-1/2+1/3-1/4+...+1/49-1/50
2) Tính: 3/2^2 . 8/3^2 . 15/4^2 . .... . 899/30^2
GIÚP MÌNH VỚI THỨ HAI PHẢI NỘP RỒI!!!!
HELP ME!!!
thực hiện phép tính
\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+50}\)
Cho day phan so:
\(\frac{1}{1};\frac{1}{2};\frac{2}{1};\frac{1}{3};\frac{2}{2};\frac{3}{1};\frac{1}{4};\frac{2}{3};\frac{3}{2};\frac{4}{1}\)
Tim ra phan so 50 cua day so tren
1 CM
a, \(\left(\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{2n-1}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{2n}\right)=\dfrac{1}{n+1}+\dfrac{1}{n+2}+...+\dfrac{1}{2n}\)( n∈Z)
b, \(\dfrac{1}{26}+\dfrac{1}{27}+...+\dfrac{1}{50}=\dfrac{99}{50}-\dfrac{97}{49}+...+\dfrac{7}{4}-\dfrac{5}{3}+\dfrac{3}{2}\)
Cho M =\(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}\) .Hãy chứng minh M<\(\frac{3}{16}\)
Câu 2 Chứng minh rằng :
\(\frac{1}{7^2}-\frac{1}{7^4}+...+\frac{1}{7^{98}}-\frac{1}{7^{100}}< \frac{1}{50}\)
1)8(4x-3)-3(2-3x)=13-40x
2)10x-5(1-4x)=5x-11
3)-3(3-4x)-5(4-3x)=12x-50
Tính tổng :
a, 1+(-2)+3+(-4)+...+19+(-20)
b, 1-2+3-4+...+99-100
c, 2-4+6-8+...++48-50
d, -1+3-5+7-...+97-99
( ghi phương pháp giải nha )
