Tính tổng 1.3.5 + 3.5 .7 +5.7 .9+ ... + 95.97.99
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
5 tháng 4 2018
A=1.3+3.5+5.7+...+99.101
6A=1.3(5+1)+3.5(7-1)+5.7(9-3)+7.9(11-5)+...+99.101(103-97)
= 1.3.5+1.3+3.5.7-3.5+5.7.9-3.5.7+7.9.11-5.7.9+...+99.101.103-97.99.101
=1.3+99.101.103
=> A= \(\frac{1.3+99.101.103}{6}\)
15 tháng 8 2017
a. Ta có: \(A=1\cdot3+3\cdot5+5\cdot7+...+99\cdot101\)
\(\Rightarrow A=1\left(1+2\right)+3\cdot\left(3+2\right)+...+99\left(99+2\right)\)
\(\Rightarrow A=\left(1^2+3^2+5^2+...+97^2+99^2\right)+2\left(1+3+5+...+97+99\right)\)
Đặt \(M=1^2+3^2+5^2+99^2\)
\(\Rightarrow M=\left(1^2+2^2+3^2+...+100^2\right)-2^2\left(1^2+2^2+3^2+50^2\right)\)
Tính dãy tổng quát \(N=1^2+2^2+3^2+...+n^2\)
\(\Rightarrow N=1\left(0+1\right)+2\left(1+1\right)+3\left(2+1\right)+...+n[\left(n-1\right)+1]\)
\(\Rightarrow N=\left[1\cdot2+2\cdot3+...+\left(n-1\right)n\right]+\left(1+2+3+...+n\right)\)
\(\Rightarrow N=n\left(n+1\right)\cdot\left[\left(n-1\right):3+1:2\right]=n\left(n+1\right)\cdot\left(2n+1\right):6\)
Áp dụng vào M ta được:
\(M=100\cdot101\cdot201:6-4\cdot50\cdot51\cdot101:6=166650\)
\(\Rightarrow A=166650+2\left(1+99\right)\cdot50:2\)
\(\Rightarrow A=166650+5000=171650\)
Vậy \(A=171650\)
13 tháng 10 2023
a) 9 + 99 + 999 + ... + 999999
= (10 - 1) + (100 - 1) + (1000 - 1) + ... + (1000000 - 1)
= (101 + 102 + 103 + ... + 106) - (1.6)
= 1111110 - 6 = 1111104
b) 1 + 11 + 111 + ... + 1111111
= 1 + (101 + 1) + (102 + 101 + 1) + ... + (106 + 105 + 104 + 103 + 102 + 101 + 1)
= 101 . 6 + 102 . 5 + 103 . 4 + ... + 106. 1) + (1 + 1.6)
= 60 + 500 + 4000 + ... + 1000000 + 7
= 1234560 + 7 = 1234567
c) C = 1.2 + 2.3 + 3.4 + 4.5 + ... + 98.99
3C = 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 + ... + 98.99.3
3C = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 98.99.(100 - 97)
3C = 1.2.3 + 2.3.4 - 2.3.1 + 3.4.5 - 3.4.2 +...+ 98.99.100 - 98.99.97
3C = 98.99.100
C = \(\dfrac{98.99.100}{3}\) = 323400
d) D = 1.3.5 + 3.5.7 + 5.7.9 + ... + 95.97.99
8D = 1.3.5.8 + 3.5.7.8 + 5.7.9.8 + ... + 95.97.99.8
8D = 1.3.5.(7 + 1) + 3.5.7.(9 - 1) + 5.7.9.(11 - 3) + ... + 95.97.99.(101 - 93)
8D = 1.3.5.7 + 1.3.5.1 + 3.5.7.9 - 3.5.7.1 + 5.7.9.11 - 5.7.9.3 + ... + 95.97.99.101 - 95.97.99.93
8D = 1.3.5.1 + 95.97.99.101
D = \(\dfrac{1.3.5.1+95.97.99.101}{8}=15517600\)
EC
0
L
2
26 tháng 8 2017
\(G=1.3.5+3.5.7+5.7.9+...+95.97.99\)
\(G=1+99.\left(3+5+7+...+97\right)\)\
\(G=100.\left[\left(3+97\right)+\left(5+95\right)+...+\left(49+51\right)\right]\)
\(G=100.\left(100.24\right)\)
\(G=100.2400=240000\)
TS
3 tháng 10 2015
\(2A=\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{97.99}\right).2\)
\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\)
\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\)
\(2A=1-\frac{1}{99}\)
\(2A=\frac{98}{99}\)
\(A=\frac{98}{99}:2\)
\(A=\frac{49}{99}\)
\(A=1.3.5+3.5.7+5.7.9+...+95.97.99\)
\(8A=1.3.5.8+3.5.7.8+5.7.9.8+...+95.97.99.8\)
\(=1.3.5.\left(7+1\right)+3.5.7.\left(9-1\right)+5.7.9.\left(11-3\right)+...+95.97.99.\left(101-93\right)\)
\(=1.3.5+1.3.5.7-1.3.5.7+3.5.7.9-3.5.7.9+5.7.9.11-...-93.95.97.99+95.97.99.101\)
\(=1.3.5+95.97.99.101\)
\(\Rightarrow A=\frac{1.3.5+95.97.99.101}{8}=11517600\)