Ta đặt: A=\(\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+...+\frac{1}{4^{100}}\)
\(\Rightarrow4A=1+\frac{1}{4}+\frac{1}{4^2}+...+\frac{1}{4^{99}}\)
4A - A = \(1-\frac{1}{4^{100}}\)= 3A = \(\frac{4^{100}-1}{4^{100}}\)\(\Rightarrow A=\frac{4^{100}-1}{4^{100}.3}=\frac{1}{3}-\frac{1}{4^{100}.3}=\frac{1}{3}-\frac{1}{4^{100}}.\frac{1}{3}=\frac{1}{3}\left(1-\frac{1}{4^{100}}\right)\)
hết
Tính C=1/2-(1/3+2/3)+(1/4+2/4+3/4)-(1/5+2/5+3/5+4/5)+...+(1/100+2/100+...+99/100)
Tính tổng 100-(1+1/2+1/3+1/4+...+1/100)/1/2+2/3+3/4+....+99/100
Bài 4: Tính tổng 1) 1 + (-2) + 3 + (-4) + . . . + 19 + (-20) 2) 1 – 2 + 3 – 4 + . . . + 99 – 100 3) 2 – 4 + 6 – 8 + . . . + 48 – 50 4) – 1 + 3 – 5 + 7 - . . . . + 97 – 99 5) 1 + 2 – 3 – 4 + ... + 97 + 98 – 99 - 100
BÀi 4: Tính tổng
1, 1+(-2)+3+(-4)+.....19+(-20)
2, 1-2+3-4+...+99-100
3, 2-4+6-8+...+48-50
4, -1+3-5+7-.....+97-99
5, 1+2-3-4+....+97+98-99-100
Tính:
M=(1-1/2^2).(1-1/3^2).(1-1/4^2)...(1-1/49^2).(1-1/50^2)
N=(3/2-2/2^2).(4/3-2/3^2).(5/4-2/4^2)...(100/99-2/99^2).(101/100-2/100^2)
1. Tính tổng:
1/ 1 + (-2) + 3 + (-4) +...+ 19 + (-20)
2/ 1 - 2 + 3 - 4 +..+ 99 - 100
3/ 2 - 4 + 6 - 8 +...+ 48 - 50
4/ -1 + 3 - 5 + 7 -...+ 97 - 99
5/ 1 + 2 - 3 - 4 +...+ 97 + 98 - 99 - 100
TÍNH TỔNG:
1. 1+(-2)+3+(-4)+...+19+(-20)
2. 1-2+3-4+...+99-100
3. 2-4+6-8+...+48-50
4. -1+3-5+7-...+97-99
5. 1+2-3-4+...+97+98-99-100
1, Tính \(\frac{1}{2}-\left(\frac{1}{3}+\frac{2}{3}\right)+\left(\frac{1}{4}+\frac{2}{4}+\frac{3}{4}\right)-\left(\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}\right)+...+\left(\frac{1}{100}+\frac{2}{100}+\frac{3}{100}+...+\frac{99}{100}\right)\)2,Tính \(\left(1-\frac{1}{2^2}\right)x\left(1-\frac{1}{3^2}\right)x\left(1-\frac{1}{4^2}\right)x...x\left(1-\frac{1}{n^2}\right)\)
Tính tổng
1/1-2+3-4+...+99-100
2/2-4+6-8+...+48-50
3/-1+3-5+7-...+97-99
4/1+2-3-4+...+97+98-99-100
