tính I=1^2+4^2+7^2+............+100^2
tính P=1.3^3+3.5^3+5.7^3+..........+49.51^3
Tính Q=1. 99^2+2.98^2+3.97^2+......+49.51^2
Bài tập:
1. Tính A=12+42+72+...+1002
2. Tính B=1.32+3.52+5.72+...+97.992
3. Tính A=1.99+2.98+3.97+...+49.51+50.50
4. Tính B=1.3+5.7+9.11+...+97.101
5. Tính C=1.3.5-3.5.7+5.7.9-7.9.11+...-97.99.101
6. Tính D=1.99+3.97+5.95+...+49.51
7. Tính E=1.33+3.53+5.73+...+49.513
8. Tính F=1.992+2.982+3.972+...+49.512
Ai giúp mk với mk tick cho
Tính tổng:
H=1.3.5-3.5.7+5.7.9-7.9.11+...+95.97.99-97.99.101
E=1.33+3.53+5.73+...+49.513
F=1.992+2.982+3.972+...+49.512
1. Tính A = 1.99+2.98+3.97+...+49.51+50.50
2. Tính B = 1.3+5.7+9.11+...+97.101
3. Tính C = 1.3.5-3.5.7+5.7.9-7.9.11+...-97.99.101
4. Tính D = 1.99+3.97+5.95+...+49.51
5. Tính E = 1.33+3.53+5.73+...+49.513
6. Tính F = 1.992+2.982+3.972+...+49.512
ai đúng mình ủng hộ
1/ A= 1.(100-1)+2(100-2)+3.(100-3)+...+49.(100-51)+50.(100-50)
= 1.100-1+2.100 - 2.2 + 3.100 -3.3 + ...+49.100 - 49.51 + 50.100 - 50.50
= 100( 1 + 2 + 3 + ...+ 50) - ( 1 + 22 + 32 + ... + 502 )
= 127500- 42925
= 84575
2/ A= 1.3 + 5.7 + 9.11+ 13.15 + 17.19 + ... + 97. 101
= 1.3 + 5(6 + 1) +9( 6+ 5) + 13(6+9) + 17(6+13) + ... + 97(95+6)
= 3 + 5.6 + 1.5 + 9.6 + 5.9 + 13.6 + 9.13 + 17.6 + 13.17 + ... + 95.97 + 97.6
= 3 + ( 1.5 + 5.9 + 9.13 + 13.17 + ...+ 95.97) + 6( 5 + 9 + 13 + 17 + ... + 97)
= ...
=\(\frac{509447}{6}\)
Bài tập dãy số theo quy luật:
Bài 1: E= 1.3.5-3.5.7+5.7.9-7.9.11+....+49.51.53
D= 1.33 + 3.53 + 5.73 +.......+ 49.513
F= 1.992 +2 .982 + 3.972 +........+ 49.512
G= 9+99+999+.....+ 9999999999
Bài tập dãy số theo quy luật:
Bài 1: E= 1.3.5-3.5.7+5.7.9-7.9.11+....+49.51.53
D= 1.33 + 3.53 + 5.73 +.......+ 49.513
F= 1.992 +2 .982 + 3.972 +........+ 49.512
G= 9+99+999+.....+ 9999999999
Giải giúp hộ
a) tính giá trị của biểu thức D=3/1.3+3/3.5+3/5.7+...+3/49.51
b) CMR : S=1+1/2^2+1/3^2+1/4^2+...+1/100^2 <2
Tính
E = 1.33 +3.53 + 5.73 +......+ 49.513
F=1.992 +3.972+ 5.952 +.........+50.512
Tính:
A = \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\)
B = \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{100}}\)
Các bạn giúp mình với, mình đang cần lắm.
Ta có:
\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\)
\(\Rightarrow2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\)
\(=1-\frac{1}{51}=\frac{50}{51}\)
\(\Rightarrow A=\frac{50}{51}:2=\frac{25}{51}\)
tính tổng :
p= 2/1.3+2/3.5+2.5.7+....................+ 2/49.51
q= 1/1.3+1/3.5+................................... +1/19.21
P = 2/1.3 + 2/3.5 + 2/5.7 + ... + 2/49.51
P = 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/49 - 1/51
P = 1 - 1/51
P = 50/51
Q = 1/1.3 + 1/3.5 + ... + 1/19.21
Q = 1/2 .(2/1.3 + 2/3.5 + ... + 2/19.21)
Q = 1/2.(1 - 1/3 + 1/3 - 1/5 + ... + 1/19 - 1/21)
Q = 1/2 . (1 - 1/21)
Q = 1/2. 20/21
Q = 10/21
Ủng hộ mk nha ^_-
\(P=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\)
\(P=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\)
\(P=1-\frac{1}{51}\)
\(P=\frac{50}{51}\)
\(Q=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{19.21}\)
\(Q=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{19.21}\right)\)
\(Q=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(Q=\frac{1}{2}.\left(1-\frac{1}{21}\right)\)
\(Q=\frac{1}{2}.\frac{20}{21}\)
\(Q=\frac{10}{21}\)
\(P=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\)
\(=1-\frac{1}{51}\)
\(=\frac{50}{51}\)
\(Q=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{19.21}\)
\(2Q=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{19.21}\)
\(2Q=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{21}\)
\(2Q=1-\frac{1}{21}\)
\(2Q=\frac{20}{21}\)
\(Q=\frac{20}{21}:2\)
\(Q=\frac{10}{21}\)