1/1.3.5 + 1/3.5.7 + 1/5.7.9 +.....+ 1/99.101.103

= 1/4. [4/1.3.5 + 4/3.5.7 + 4/ 5.7.9 +....+ 4/99.101.103]

=1/4. [1/1.3 - 1/3.5 + 1/3.5 - 1/5.7 +....+ 1/99.101 - 1/101.103]

= 1/4. [1/1.3 - 1/101.103]

=1/4. 10406/31209

= 5230/62418

\(A=\frac{1}{1\cdot3\cdot5}+\frac{1}{3\cdot5\cdot7}+....+\frac{1}{99\cdot101\cdot103}\)

\(2A=\frac{1}{1\cdot3}-\frac{1}{3\cdot5}+\frac{1}{3\cdot5}-\frac{1}{5-7}+....+\frac{1}{99\cdot101}-\frac{1}{101\cdot103}\)

\(2A=\frac{1}{1\cdot3}-\frac{1}{101\cdot103}\)

Tính nốt

(chỉnh đề)

A=\(-1+2-3-4-5+6-7-8-9+...-2021-2022+2023-2024\)

=\(\left(-1-2024\right)+\left(2+2023\right)+\left(-3-2022\right)+\left(-4-2021\right)+\left(-5-2020\right)+\left(6+2019\right)-\left(-7-2018\right)+\left(-8-2017\right)+\left(-9-2016\right)+...+\left(1010+1015\right)+\left(-1011-1014\right)+\left(-1012-1013\right)\)=\(-2025+2025-2025-2025-2025+2025-2025-2025-2025+...+2025-2025-2025\)=253.2025-1771.2025=-3 073 950.

B=\(1.3.5+3.5.7+5.7.9+7.9.11+...+99.101.103\)

8B=\(1.3.5.8+3.5.7.8+5.7.9.8+7.9.11.8+...+99.101.103.8\)

8B=\(1.3.5.\left[7-\left(-1\right)\right]+3.5.7.\left(9-1\right)+5.7.9.\left(11-3\right)+7.9.11.\left(13-5\right)+...+99.101.103.\left(105-97\right)\)8B=\(3.5+3.5.7+3.5.7.9-3.5.7+5.7.9.11-3.5.7.9+7.9.11.13-5.7.9.11+...+99.101.103.105-97.99.101.103\)

B=\(\dfrac{3.5+99.101.103.105}{8}=13517400\)

- Đặt C₁=\(1.3+3.5+...+197.199\).

6C₁=\(1.3.6+3.5.6+...+197.199.6\)

6C₁=\(1.3.\left[5-\left(-1\right)\right]+3.5.\left(7-1\right)+...+197.199.\left(201-195\right)\)

6C₁=\(3+3.5+3.5.7-3.5+...+197.199.201-195.197.199\)
C₁=\(\dfrac{3+197.199.201}{6}=1313301\)

- Đặt C₂=\(2.4+4.6+...+198.200\)

6C₂=\(2.4.6+4.6.6+...+198.200.6\)

6C₂=\(2.4.\left(6-0\right)+4.6.\left(8-2\right)+...+198.200.\left(202-196\right)\)

C₂=\(\dfrac{198.200.202}{6}=1333200\)

=>C₁+C₂=C=1313301+1333200=2646501

đáp án là : 35/429

các pn thân iu ơi giúp mik với nha! chìu nay mik cần r!

https://www.youtube.com/watch?v=vNJ2wLqK7Mw

lên đây tham khảo nha

c=94/285

mình cũng ko hiểu cách giải này cho lắm nên mình làm thế thôi

\(A=\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{95.97.99}\)

\(A=4.\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+\frac{1}{5.7}-\frac{1}{7.9}+...+\frac{1}{95.97}-\frac{1}{97.99}\right)\)

\(A=4.\left(\frac{1}{1.3}-\frac{1}{97.99}\right)\)

\(A=4.\frac{3200}{9603}=\frac{12800}{9603}\)

\(A=\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{95.97.99}\)

\(A=\frac{1}{4}.\left(\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{95.97.99}\right)\)

\(A=\frac{1}{4}.\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+\frac{1}{5.7}-\frac{1}{7.9}+...+\frac{1}{95.97}-\frac{1}{97.99}\right)\)

\(A=\frac{1}{4}.\left(\frac{1}{1.3}-\frac{1}{97.99}\right)\)

\(A=\frac{1}{4}.\frac{3200}{9603}\)

\(A=\frac{800}{9603}\)

Bài trc mik làm lộn :)))
~ Hok tốt ~