K
Khách

Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.

27 tháng 9 2018

A = 1.2 + 2.3 + ... + 99.100

3A = 1.2.3 + 2.3.(4-1) + ... + 99.100.(101-98)

3A = 1.2.3 + 2.3.4 - 1.2.3 + ... + 99.100.101 - 98.99.100

3A = 99.100.101

3A = 999900

A = 333300

C = 1.2.3 + 2.3.4 + ... + 49.50.51

4C = 1.2.3.4 + 2.3.4.(4-1) + ... + 49.50.51.(52-48)

4c = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + ... + 49.50.51.52 - 48.49.50.51

4C = 49.50.51.52

4C = 6497400

C = 1624350

27 tháng 9 2018

Ta có :

a=1.2+2.3+3.4+...+99.100

3a=1.2.3+2.3.3+3.4.3+...+99.100.3

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

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

3a=99.100.101

a=\(\frac{99.100.101}{3}\)

a=333300

Tính c làm tương tự

14 tháng 6 2020

\(A=\frac{4}{1.2}+\frac{4}{2.3}+\frac{4}{3.4}+...+\frac{4}{2019.2020}\)

\(\frac{1}{4}A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2019.2020}\)

\(\frac{1}{4}A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2019}-\frac{1}{2020}\)

\(\frac{1}{4}A=1-\frac{1}{2020}=\frac{2019}{2020}\)

\(\Rightarrow A=\frac{2019}{2020}:\frac{1}{4}=\frac{2019}{505}\)

Vậy \(A=\frac{2019}{505}.\)

\(B=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{98.99.100}\)

\(\Rightarrow2B=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{98.99.100}\)

\(2B=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{98.99}-\frac{1}{99.100}\)

\(2B=\frac{1}{1.2}-\frac{1}{99.100}=\frac{4949}{9900}\)

\(\Rightarrow B=\frac{4949}{9900}:2=\frac{4949}{19800}\)

Vậy \(B=\frac{4949}{19800}.\)

14 tháng 6 2020

\(A=\frac{4}{1\cdot2}+\frac{4}{2\cdot3}+\frac{4}{3\cdot4}+...+\frac{4}{2019\cdot2020}\)

\(A=4\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2018\cdot2019}\right)\)

\(A=4\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2018}-\frac{1}{2019}\right)\)

\(A=4\left(1-\frac{1}{2019}\right)=4\cdot\frac{2018}{2019}\)

Đến đây tự tính

\(B=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{98\cdot99\cdot100}\)

\(B=\frac{1}{2}\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{98\cdot99\cdot100}\right)\)

\(B=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+...+\frac{1}{98\cdot99}-\frac{1}{99\cdot100}\right)\)

\(B=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{99\cdot100}\right)=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{9900}\right)\)

Số hơi bị dữ nên tính nốt nhé

Bài 5:

a) Ta có: \(A=1\cdot2+2\cdot3+3\cdot4+...+9\cdot10\)

\(\Leftrightarrow3\cdot A=3\cdot\left(1\cdot2+2\cdot3+3\cdot4+...+9\cdot10\right)\)

\(\Leftrightarrow3A=1\cdot2\cdot\left(3-0\right)+2\cdot3\cdot\left(4-1\right)+3\cdot4\cdot\left(5-2\right)+...+9\cdot10\cdot\left(11-8\right)\)

\(\Leftrightarrow3A=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+3\cdot4\cdot5-2\cdot3\cdot4+...+8\cdot9\cdot10-8\cdot9\cdot10+9\cdot10\cdot11\)

\(\Leftrightarrow3\cdot A=9\cdot10\cdot11=90\cdot11=990\)

hay A=330

Vậy: A=330

21 tháng 7 2017

c, 4C= (1.2.3+2.3.4+3.4.5+...+8.9.10) .4

==> 4C= [1.2.3.(4-0) + 2.3.4-(5-1) + 8.9.10.(11-7)

==>4C= 1.2.3.4 - 1.2.3.4+ 2.3.4.5-2.3.4.5 + 7.8.9.10- 7.8.9.10 + 8.9.10.11

==> 4C= 8.9.10.11=7920

==> C= 7920 :4=1980

a, Ta có: 3A= 1.2.3+2.3.3+3.4.3+...+99.100.3

               3A=1.2.(3-0) + 2.3.(4-1)+ 3.4.(5-2)+ ... + 99.100.( 101-98)

               3A=(1.2.3 + 2.3.4+ 3.4.5+ 99.100.101) - (0.1.2 +1.2.3+ 2.3.4 + ... + 98.99.100)

               3A= 99.100.101 - 0.1.2

               3A= 999900 - 0

               3A= 999900

    ==> A= 999900 : 3

   ==> A= 333300

16 tháng 2 2021

https://olm.vn/hoi-dap/tim-kiem?q=t%C3%ADnh+t%E1%BB%95ng+sau+:S+=+1.2.3+2.3.4+3.4.5+...+n.(n+1).(n+2)+&id=601088

30 tháng 1 2020

\(A = 1.2+2.3+3.4+4.5+...+99.100\)

\(3A= 1.2.3+2.3.3+3.4.3+4.5.3+\)\(...+\)

\(99.100.3\)

\(3A = 1.2.3+2.3.(4-1)+3.4. (5-2)+\)

\(4.5. (6-3)+...+99.100. (101-98)\)

\(3A = 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+\)

\(4.5.6-3.4.5+...+99.100.101-98.99.100\)

\(3A = 99 .100 .101\)

\(A = 99 .100 . 101 ÷ 3 \)

\(A = 333300\)

A = 1.2 + 2.3 + 3.4 + ....... + 99.100
3A = 1.2.3 + 2.3.3 + 3.4.3 + ....... + 99 . 100 . 3
3A = 1.2.3 + 2.3.(4-1) + 3.4.(5-2) +.... + 99.100.(101-98)
3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ..... + 99 . 100 . 101 - 98 . 99 . 100
3A = (1.2.3 - 1.2.3) + (2.3.4-2.3.4) + ... + (98.99.100 - 98.99.100) + 99 . 100 . 101
3A = 99 . 100 . 101 = 999900
A = 999900 : 3 = 343400

# Học tốt☘️#

Câu 1: 

Đặt S = 1.2+2.3+3.4+...+30.31

  3 S  = 1.2.3+2.3.3+3.4.3+...+30.31.3

  3 S  = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2) + ...+ 30.31.(32-29)

  3S  = 1.2.3 + 2.3.4-2.3 + 3.4.5-2.3.4 + ...+ 30.31.32-29.30.31

  3S= 30.31.32 

S= 30.31.32/3

DD
3 tháng 8 2021

\(E=\frac{1}{1.2}-\frac{1}{1.2.3}+\frac{1}{2.3}-\frac{1}{2.3.4}+....+\frac{1}{99.100}-\frac{1}{99.100.101}\)

\(=\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\right)-\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{99.100.101}\right)\)

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}=\frac{99}{100}\)

\(B=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{99.100.101}\)

\(=\frac{1}{2}\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+...+\frac{101-99}{99.100.101}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{99.100}-\frac{1}{100.101}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{100.101}\right)=\frac{5049}{20200}\)

Suy ra \(E=A-B=\frac{99}{100}-\frac{5049}{20200}=\frac{14949}{20200}\)

4 tháng 8 2021

\(\frac{14949}{20200}\)

9 tháng 3 2018

A) \(A=1+4+4^2+4^3+...+4^{26}\)

\(\Rightarrow4A=4+4^2+4^3+4^4+...+4^{27}\)

\(\Rightarrow4A-A=4^{27}-1\)

\(3A=4^{27}-1\)

\(A=\frac{4^{27}-1}{3}\)

B) \(B=3+3^3+3^5+3^7+...+3^{21}\)

\(\Rightarrow3^2B=3^3+3^5+3^7+3^9+...+3^{23}\)

\(\Rightarrow3^2B-B=3^{23}-3\)

\(8B=3^{23}-3\)

\(B=\frac{3^{23}-3}{8}\)

C) \(M=1.2+2.3+3.4+...+49.50\)

\(\Rightarrow3M=1.2.3+2.3.3+3.4.3+...+49.50.3\)

\(3M=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+49.50.\left(51-48\right)\)

\(3M=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+49.50.51-48.49.50\)

\(3M=\left(1.2.3+2.3.4+3.4.5+...+49.50.51\right)-\left(1.2.3+3.4.5+...+48.49.50\right)\)

\(3M=49.50.51\)

\(M=\left(49.50.51\right):3\)

\(M=41650\)

D) \(N=1.2.3+2.3.4+3.4.5+...+49.50.51\)

\(\Rightarrow4N=1.2.3.4+2.3.4.4+3.4.5.4+...+49.50.51.4\)

\(4N=1.2.3.\left(4-0\right)+2.3.4\left(5-1\right)+3.4.5.\left(6-2\right)+...+49.50.51.\left(52-48\right)\)

RỒI BN LÀM GIỐNG NHƯ MK Ở PHẦN C THÌ NÓ SẼ RA!

CHÚC BN HỌC TỐT!!!!