Question

Tính:

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

B=1.3.5+3.5.7+5.7.9+7.9.11+...+99.101.103

C=1.3+2.4+3.5+...+198.200

 

Answer 1

(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.

Answer 2

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

Answer 3

- 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