Tính nhanh :
1) 99^2+99.2+1
2) (10^2+8^2+6^2+4^2+2^2)-(9^2+7^2+5^2+3^2+1)
3) 2020^2-2019.(2020+1)
4) 3.(2^2+1)….(2^2020+1)
Tính nhanh : 1) 99^2+99.2+1 2) (10^2+8^2+6^2+4^2+2^2)-(9^2+7^2+5^2+3^2+1) 3) 2020^2-2019.(2020+1) 4) 3.(2^2+1)….(2^2020+1)
By Peyton
Đáp án:
Giải thích các bước giải:
1, 99² + 99.2 + 1
= (99+1)²
=100²
=10000
2, ( 10² + 8² + 6² + 4² + 2²) – (9² + 7² + 5² + 3² + 1²)
= 10² + 8² + 6² + 4² + 2² – 9² – 7² – 5² – 3² – 1²
= (10² – 9²) + (8² – 7²) + (6² – 5²) + (4²- 3²) + (2²-1²)
=(10-9)(10+9) + (8-7)(8+7) + (6-5)(6+5) + (4-3)(4+3) + (2-1)(2+1)
=10+9+8+7+6+5+4+3+2+1
=(10+1).10/2
=55
3, 2020²- 2019(2020+1)
=2020² – 2019.2020 – 2019
= 2020(2020-2019)-2019
=2020 – 2019
=1
4, 3(2²+1)(2^4+1)…(2^2018+1)(2^2020+1)
=(2²-1)(2²+1)(2^4+1)…(2^2018+1)(2^2020+1)
=(2^4-1)(2^4+1)…(2^2018+1)(2^2020+1)
….
=2^4040-1