Question

Find the given sum:
(60² - 59²) + (58² - 57²) + (56² - 55²) + .... + (2² - 1²)

Answer 1

Answer:

1830

Step-by-step explanation:

Hi,

Given (60² - 59²) + (58² - 57²) + (56² - 55²) + .... + (2² - 1²)

Using a² - b² = (a - b) (a + b)

We can write (60² - 59²) = (60 - 59)*(60 + 59)

= 1*(60 + 59)-------(1)

(58² - 57²) = (58 - 57)*(58 + 57)

= (58 + 57)--------(2)

56² - 55² = (56 - 55)*(56 + 55)

= (56 + 55)-------(3)

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(2² - 1²) = (2 - 1)*(2 + 1)-----(4)

If we substitute the results from (1), (2), (3) and (4) ,

we get the given sum

= (1)[ 60 + 59 + 58 + 57 +......+2 + 1]

Sun of first 60 natural numbers

= 60*(60 + 1)/2

= 1830

Hope, it helps !