Tính hợp lý:
a)A=1.2.3+2.4.6+3.6.9+5.10.15/ 1.3.5+2.6.14+3.9.21+5.25.35
b)B=(1+1/1.3)+(1+1/2.4+)+....+(1+1/99.101)
c)C=1+(1+2)+(1+2+3)+...+(1+2+3+4+....+99+100)/1.100+ 2.99+ 3.98+....+100.1
Bạn nào làm hết và đúng, nhanh mik sẽ tick nhé =))
Tính hợp lí:
A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128
C = 22/3 . 32/2.4 . 42/3.5 ... 592/58.60
D = 6/1.3 + 6/3.5 + 6/5.7 + ... + 6/2009.2011
E = \(\frac{1.2.3+2.4.6-3.6.9+5.10.15}{1.3.7+2.6.14-3.9.21+5.15.35}\)
F = (1+1/2).(1+1/3).1+1/4)...(1+1/100)
G = 5 - 52/1.6 - 52/6.11 - ... - 52/101.106.
A = 1/2 + 1/4 + 1/8 + ... + 1/128
A = 1/2^1 + 1/2^2 + 1/2^3 + ... + 1/2^7
2A = 1 + 1/2 + 1/2^2 + ... + 1/2^6
2A - A = 1 - 1/2^7 = A
G = 5 - 5^2/1*6 5^2/6*11 - ... - 5^2/101*106
G = -5(-1 + 5/1*6 + 5/6*11 + ... + 5/101*106)
G = -5(-1 + 1 - 1/6 + 1/6 - 1/11 + ... + 1/101 - 1/106)
G = -1.(-1/106)
G = 1/106
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(2A-A=1-\frac{1}{128}\)
\(A=\frac{127}{128}\)
Tính các tổng sau:
1.100+2.99+3.98+...+98.3+99.2+100.19+99+999+....+999...9991.2+2.3+3.4+...+n(n+1)2.4+4.6+6.8+....+2n(2n+2)1.3+2.4+3.5+...+n(n+2)1.2.3+2.3.4+3.4.5+....+n(n+1).(n+2)12+22+32+...+n2\(S=\frac{40404}{70707}+\frac{1952.395-1208}{1708+395.1701}+\frac{1.2.3+2.4.6+3.6.9+5.10.15}{1.3.7+2.6.14+3.9.21+5.15.35}\)
Thực hiện phép tính:
a, A=1/2+1/14+1/35+1/65+1/104+1/152+1/209
b, 1010/1008.8-994-1.2.3+2.4.6+3.6.9+5.10.15/1.3.6+2.6.12+3.9.18+5.10.30
c, 1/1.2.3+1/2.3.4+1/3.4.5+...+1/10.11.12
Tính tổng : B = 12 + 22 + 32 + ... + 992 + 1002
C = 1012 + 1022 + ... + 1992 + 2002
D = 1.3 + 2.4 + 3.5 + 4.6 + ... + 99.100 +1010.102
T = 1.100 + 2.99 + 3.98 + ... + 99.2 + 100.1
S = 1.2.3 + 2.3.4 + 3.4.5 + ... + 98.99.100
Giúp mk nha các bạn!
Giải:
a, \(B=1^2+2^2+3^2+...+99^2+100^2.\)
\(B=1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+...+99\left(100-1\right)+100\left(101-1\right).\)
\(B=1.2-1.1+2.3-1.2+3.4-1.3+...+99.100-1.99+100.101-1.100.\)
\(B=\left(1.2+2.3+3.4+...+99.100+100.101\right)-\left(1+2+3+...+100\right).\)
\(B=\dfrac{\left[1.2.3+2.3\left(4-1\right)+3.4\left(5-2\right)+...+100.101\left(102-99\right)\right]}{3}+\dfrac{100\left(100+1\right)}{2}.\)
\(B=\dfrac{\left(1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+100.101.102-99.100.101\right)}{3}+5050.\)
\(B=\dfrac{100.101.102}{3}+5050.\)
\(B=343400+5050=348450.\)
Vậy \(B=348450.\)
\(C=...\) (làm tương tự con \(B\)).
\(D=...\) (hình như đề sai).
\(T=1.100+2.99+3.98+...+99.2+100.1.\)
\(T=1.100+2.\left(100-1\right)+3.\left(100-2\right)+...+99\left(100-98\right)+100\left(100-99\right).\)
\(T=1.100+100.2+1.2+100.3+2.3+...+100.99+98.99+100.100+99.100.\)
\(T=100\left(1+2+3+...+100\right)-\left(1.2+2.3+3.4+...+99.100\right).\)
\(T=100.\dfrac{100.101}{2}-\dfrac{99.100.101}{3}.\)
\(T=100.5050-333300.\)
\(T=505000-333300=171700.\)
Vậy \(T=171700.\)
\(S=1.2.3+2.3.4+3.4.5+...+98.99.100.\)
\(4S=4\left(1.2.3+2.3.4+3.4.5+...+98.99.100\right).\)
\(4S=1.2.3.4+2.3.4.4+3.4.5.4+...+98.99.100.4.\)
\(4S=1.2.3\left(5-1\right)+2.3.4\left(6-2\right)+...+98.99.100\left(101-97\right).\)
\(4S=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...+98.99.100.101-97.98.99.100.\)
\(4S=\left(1.2.3.4-1.2.3.4\right)+\left(2.3.4.5-2.3.4.5\right)+...+\left(97.98.99.100-97.98.99.100\right)+98.99.100.101.\)
\(4S=0+0+...+0+98.99.100.101.\)
\(4S=98.99.100.101.\)
\(4S=97990200.\)
\(\Rightarrow S=\dfrac{97990200}{4}=24497550.\)
Vậy \(S=24497550.\)
~ Học tốt!!! ~
Tổng của B ;
\(SUM\left(B\right)=\sum\limits^{100}_{x=1}\left(x^2\right)=338350\)
Tổng của C :
\(SUM\left(C\right)=\sum\limits^{200}_{x=101}\left(x^2\right)=2348350\)
Tính
a, D= 1.2 +2.3 +3.4+...+99.100
Kết quả là bằng 33100101
b, sử dụng kết quả câu a tính
E=1+2²+3²+...+98²+99²
c, tính
F= 1.100+2.99+3.98+...+99.2+100.1
d, tính
G=1.2.3+2.3.4+...+ 48.49.50
e, tính
H= 1+2+4+8+16+...+8192
2, cho A= 1+2+2²+3²+...+200²
Hãy viết A+1 dưới dạng 1 lũy thừa
3, cho B= 3+3²+3³+...+3^2005
Chứng tỏ 2.B+3 là lũy thừa của 3
C= 4+2²+2³+...+2^2005
Chứng tỏ C là 1 lũy thừa của 2
tính tổng B=\(1^2+2^2+3^2+....+99^2+100^2\)
tính tổng C=\(101^2+102^2+103^2+....+199^2+200^2\)
tính tổngT=1.100+2.99+3.98+....+99.2+100.1
\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+4+...+100\right)}{1.100+2.99+3.98+4.96+...+100.1}\)
Tính:
E = 1^2 + 2^2 + 3^2 +...+ 98^2 + 99^2
F = 1.100 + 2.99 + 3.98 +...+ 98.3 + 99.2 + 100.1