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2-3+4-5+6-7...-99+100?

asked Feb 4, 2013 in ALGEBRA 2 by anonymous Apprentice

1 Answer

+4 votes

2 - 3 + 4 - 5 + 6 - 7..... - 99 + 100 = ?

(2 + 4 + 6+ .............+ 98) - (3 + 5 + 7 +............... + 99) + 100

Write the expression the different sum of even numbers and sum of odd numbers.

sum of even numbers = ∑ 2n                              where n = 49

sum of odd numbers = ∑(2n + 1)                        where n = 49

i.e. ∑ [(2n) - (2n + 1)] + 100

∑ [(2n - 2n - 1)] + 100

=> ∑ (-1) + 100 = -n + 100

So, 49 terms gives => -49 + 100 = 51

Therefore 2-3+4-5+6-7........ -99+100 = 51.

answered Feb 4, 2013 by richardson Scholar

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