45^2-43^2+44^2-42^2+43^2-41^2+42^2-40^2. ...till 15 terms is
Answers
Answered by
31
45² - 43² + 44² - 42² + 43² - 41² + 42² - 40² ....till 15 terms is
we can write as 45² - 43² + 44² - 42² + 43² - 41² + 42² - 40² + 41² - 39² + 40² - 38² + 39² - 37² + 38²
= (38² + 39² + 40² + 41² + 42² + 43² + 44² + 45² ) - (37² + 38² + 39² + 40² + 41² + 42² + 43²)
= 44² + 45² - 37²
= 45² + 44² - 37²
= 1225 + (44 - 37) × (44 + 37)
= 1225 + 7 × 81
= 1225 + 567
= 1792
we can write as 45² - 43² + 44² - 42² + 43² - 41² + 42² - 40² + 41² - 39² + 40² - 38² + 39² - 37² + 38²
= (38² + 39² + 40² + 41² + 42² + 43² + 44² + 45² ) - (37² + 38² + 39² + 40² + 41² + 42² + 43²)
= 44² + 45² - 37²
= 45² + 44² - 37²
= 1225 + (44 - 37) × (44 + 37)
= 1225 + 7 × 81
= 1225 + 567
= 1792
Answered by
1
Step-by-step explanation:
1792....................
Similar questions