tính tổng A=1.2+2.3+3.4+...+98.99
B=12+22+32+...+982
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26 tháng 9 2021
\(a,A=1\cdot2+2\cdot3+...+98\cdot99\\ 3A=1\cdot2\cdot3+2\cdot3\cdot3+3\cdot4\cdot3+...+98\cdot99\cdot3\\ 3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+3\cdot4\left(5-2\right)+...+98\cdot99\left(100-97\right)\\ 3A=1\cdot2\cdot3-1\cdot2\cdot3+2\cdot3\cdot4-2\cdot3\cdot4+3\cdot4\cdot5-...-97\cdot98\cdot99+98\cdot99\cdot100\\ 3A=98\cdot99\cdot100=970200\\ A=323400\)
\(b,B=1^2+2^2+3^3+...+98^2\\ B=1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+...+98\left(99-1\right)\\ B=\left(1\cdot2+2\cdot3+3\cdot4+...+98\cdot99\right)-\left(1+2+...+98\right)\\ B=323400-\left[\left(98+1\right)\left(98-1+1\right):2\right]\\ B=323400-4851=318549\\ c,C=1\cdot99+2\left(99-1\right)+3\left(99-2\right)+...+98\left(99-97\right)+99\left(99-98\right)\\ C=1\cdot99+2\cdot99-1\cdot2+3\cdot99-2\cdot3+...+98\cdot99-97\cdot98+99\cdot99-98\cdot99\\ C=99\left(1+2+...+99\right)-\left(1\cdot2+2\cdot3+...+98\cdot99\right)\\ C=99\left[\left(99+1\right)\left(99-1+1\right):2\right]-323400\\ C=490050-323400=166650\)
26 tháng 9 2021
https://hoc24.vn/cau-hoi/a-tinh-tong-a1223349899b-su-dung-ket-qua-cau-a-tinh-b122232972982c-su-dung-ket-qua-cau-a-tinh-c1992983979829.2030286199021
:vv hỏi hoài z?
HL
1
31 tháng 1
\(A=1\cdot2+2\cdot3+...+151\cdot152\)
\(=1\left(1+1\right)+2\left(1+2\right)+...+151\left(1+151\right)\)
\(=\left(1+2+3+...+151\right)+\left(1^2+2^2+...+151^2\right)\)
\(=\dfrac{151\left(151+1\right)}{2}+\dfrac{151\left(151+1\right)\left(2\cdot151+1\right)}{6}\)
\(=151\cdot76+\dfrac{151\cdot152\cdot303}{6}\)
\(=151\cdot76+151\cdot7676=1170552\)
\(C=2\cdot4+4\cdot6+...+2024\cdot2026\)
\(=2\cdot2\left(1\cdot2+2\cdot3+...+1012\cdot1013\right)\)
\(=4\left[1\left(1+1\right)+2\left(1+2\right)+...+1012\left(1+1012\right)\right]\)
\(=4\left[\left(1+2+...+1012\right)+\left(1^2+2^2+...+1012^2\right)\right]\)
\(=4\left[1012\cdot\dfrac{1013}{2}+\dfrac{1012\left(1012+1\right)\left(2\cdot1012+1\right)}{6}\right]\)
\(=4\left[506\cdot1013+345990150\right]\)
\(=1386010912\)
\(M=1^2+2^2+...+2024^2\)
\(=\dfrac{2024\left(2024+1\right)\cdot\left(2\cdot2024+1\right)}{6}\)
\(=2024\cdot2025\cdot\dfrac{4049}{6}\)
=2765871900
\(N=1^3+2^3+...+100^3\)
\(=\left(1+2+3+...+100\right)^2\)
\(=\left[\dfrac{100\left(100+1\right)}{2}\right]^2\)
\(=\left[50\cdot101\right]^2=5050^2\)
\(Q=1^3+2^3+...+2024^3\)
\(=\left(1+2+3+...+2024\right)^2\)
\(=\left[\dfrac{2024\left(2024+1\right)}{2}\right]^2\)
\(=\left[1012\left(2024+1\right)\right]^2\)
\(=2049300^2\)
TT
1
12 tháng 3 2018
BÀI 1:
\(S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(S=1+\frac{1}{1.2}+\frac{1}{2.2}+\frac{1}{2.4}+\frac{1}{4.4}+\frac{1}{4.8}\)
\(S=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}\)
\(S=1+1-\frac{1}{8}\)
\(S=\frac{15}{8}\)
BÀI 2:
\(A=1.2+2.3+3.4+...+98.99\)
\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+...+98.99.3\)
\(3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+98.99.\left(100-97\right)\)
\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+98.99.100-97.98.99\)
\(3A=\left(1.2.3+2.3.4+3.4.5+98.99.100\right)-\left(1.2.3+2.3.4+...+97.98.99\right)\)
\(3A=98.99.100\)
\(3A=970200\)
\(\Rightarrow A=970200:3\)
\(A=323400\)
CHÚC BN HỌC TỐT!!!
7 tháng 12 2023
A = 1.2 + 2.3 + 3.4 + ... + 2013.2014
3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 2013.2014.3
Mà :
1.2.3 = 1.2.3
2.3.3 = 2.3.4 - 2.3.1
3.4.3 = 3.4.5 - 3.4.2
2012.2013.3 = 2012.2013.2014 - 2012.2013.2011
2013.2014.3 = 2013.2014.2015 - 2013.2014.2012
Cộng tất cả, vế theo vế ---> 3S = 2013.2014.2015
---> A = 2013.2014.2015 / 3 = 2723058910.
của bạn đây
28 tháng 6 2016
Tính tổng : A=1.2+2.3+3.4+..+19.20
3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ..... + 19.20.21
3A = 19.20.21
A = \(\frac{19.20.21}{3}=3990\)
28 tháng 6 2016
Tính tổng : A=1.2+2.3+3.4+..+19.20
3a=1.2.3-1.2.3.+2.3.4-2.3.4+......+19.20.21
3a=19.20.21
a=19.20.21:3=3990
8 tháng 11 2016
3S=1.2.3+2.3.3+3.4.3+...+49.50.3
=1.2.3+2.3.(4-1)+3.4.(5-2)+...+48.49.(50-47)+49.50.(51-48)
=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+48.49.50-47.48.49+49.50.51-48.49.50
=(1.2.3-1.2.3)+(2.3.4-2.3.4)+...(47.48.49-47.48.49)-(48.49.50-48.49.50)+49.50.51
=0+0+...+0+0+49.50.51
=49.50.51
\(S=\frac{\left(49.50.51\right)}{3}\)
=41650
Đáp số:41650
8 tháng 11 2016
3A=1.2.3+2.3.3+..............+150.151.3
=1.2.3+2.3.(4-1)................+150.151.(152-149)
=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+....................+150.151.152-149.150.151
=150.151.152
=>A=\(\frac{150.151.152}{3}\)
A=1147600
thấy ổn thì t nhé
A=98.99.100/3 = 323400
B=98.99/2 =4851