TRONG QUYỂN NÂNG CAO PHÁT TRIỂN TOÁN 6 CÓ ĐẤY

Bạn lấy số cuối dãy trừ số đầu dãychia khoảng cách la 1 va tru 1 la tim ra so phan tu

Roi ban lay so dau day cong so cuoi daycong phan tu ban vua tinh ra chia 2

Đặt A = 10.11 + 11.12 + ... + 29.30

ta có : 3A = 10.11.3 + 11.12.3 + ... + 29.30.3 

3A = 10.11.(12-9) + 11.12.(13-10) + ... + 29.30.(31-28) 

3A = 10.11.12 - 9.10.11 + 11.12.13 - 10.11.12+ ... + 29.30.31 - 28.29.30 

3A = (10.11.12 + 11.12.13 + ... + 29.30.31) - (9.10.11 + 10.11.12 + ... + 28.29.30) 

3A = 29.30.31 - 9.10.11 

3A = 26970 - 990

3A = 25980

A = 25980 : 3 

A = 8660

Vậy A = 8660 

\(A=10\cdot11+11\cdot12+12\cdot13+...+29\cdot30\\ 3A=10\cdot11\cdot3+11\cdot12\cdot3+12\cdot13\cdot3+...+29\cdot30\cdot3\\ 3A=10\cdot11\cdot\left(12-9\right)+11\cdot12\cdot\left(13-10\right)+12\cdot13\cdot\left(14-11\right)+...+29\cdot30\cdot\left(31-28\right)\\ 3A=10\cdot11\cdot12-9\cdot10\cdot11+11\cdot12\cdot13-10\cdot11\cdot12+12\cdot13\cdot14-11\cdot12\cdot13+...+29\cdot30\cdot31-28\cdot29\cdot30\\ 3A=\left(10\cdot11\cdot12-10\cdot11\cdot12\right)+\left(11\cdot12\cdot13-11\cdot12\cdot13\right)+...+\left(28\cdot29\cdot30-28\cdot29\cdot30\right)+29\cdot30\cdot31-9\cdot10\cdot11\\ 3A=29\cdot30\cdot31-9\cdot10\cdot11\\ A=\dfrac{29\cdot30\cdot31-9\cdot10\cdot11}{3}\\ A=\dfrac{3\cdot\left(29\cdot10\cdot31-3\cdot10\cdot11\right)}{3}\\ A=29\cdot10\cdot31-3\cdot10\cdot11\\ A=10\cdot\left(29\cdot31-3\cdot11\right)\\ A=10\cdot866\\ A=8660\)

Cảm ơn bạn !

\(S=9\cdot10+10\cdot11+11\cdot12+...+99\cdot100\)

\(3S=9\cdot10\cdot3+10\cdot11\cdot3+11\cdot12\cdot3+...+99\cdot100\cdot3\)

\(3S=9\cdot10\cdot\left(11-8\right)+10\cdot11\cdot\left(12-9\right)+...+99\cdot100\cdot\left(101-98\right)\)

\(3S=9\cdot10\cdot11-8\cdot9\cdot10+10\cdot11\cdot12-9\cdot10\cdot11+...+99\cdot100\cdot101-98\cdot99\cdot100\)

\(3S=99\cdot100\cdot101\)

\(S=\frac{99\cdot100\cdot101}{3}=333300\)

tổng này có:99-10+1=90 so hang

(10,10+99,99)x90:2=4954,05

k nhe

3N = 1.2.3+2.3(4-1)+3.4.(5-2)+.+99.100.(101-98)

3N = 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+.+99.100.101-98.99.100

3N = 99.100.101

3N=33.100.101=333300

b)

tổng này có  99-10+1=90 (số hạng):

10,11 + 11,12 + 12,13 +............+ 98,99 + 99,100 =

10,100 + 11,11 + 12,12 + .......... + 98,98 + 99,99 =

(10,10 + 99,99) x 90 : 2 = 4954,05

c)

R=1.(2-1)+2.(3-1)+.....+100.(101-1)

=1.2-1.1+2.3-1.2+......+100.101-1.100

=(1.2+2.3+.....+99.100+100.101)-(1+2+3+...+100)

=[1.2.3+2.3.(4-1)+........100.101.(102-99)]:3+[(100+1).100:2]

(tổng trên chia cho 3 nên cuối cùng chia 3)

=(1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+.....100.101.102-99.100.101):3+5050

=(100.101.102) :3 +5050

=348450

d)=1.100+2.(100-1)+.....+100.(100-99)

=1.100+2.100-1.2+3.100-2.3+........+100.100-99.100

=100.(1+2+3+.......+100)-(1.2+2.3+3.4+....+99.100)

=100.\(\frac{101.100}{2}-\frac{99.100.101}{3}\) =505000-333300=171700

p/s mỏi tay, bấm mình nhé

A = (1.2+2.3+...+29.30)-(1.2+2.3+...+9.10) = B - C 

Áp dụng công thức:S = 1.2 + 2.3 +  … + (n - 1).n = (n - 1).n.(n + 1)/3 có: B =8990; C =330

Suy ra: A = 8660