An algebra problem by أحمد الحلاق

Algebra Level 3

$\large 1^2 + 2^2 - 3^2 - 4^2 + 5^2 + 6^2 - 7^2 - 8^2 + \cdots - 1000^2 + 1001^2 = \, ?$

-999 998 -998 1002 1001

1 solution

A Former Brilliant Member
Sep 30, 2016

$\implies A= 1^2 +(2^2 - 3^2)+ (- 4^2 + 5^2) + (6^2 - 7^2)+( - 8^2 + 9^2)+ \cdots +(- 1000^2 + 1001^2)$

$A=1+(5×-1)+(9×1)+(13×-1)+(17×1)+ ... +(2001×1)$

$A=(1-5)+(9-13)+17+...+2001$

$A=-(\underbrace{4+4+4+4+...}_{250 \ \text{times}})+2001$

$A=-(4×250)+2001$

$A=2001-1000=\boxed{1001}$

can you help me please??

Charlene Galvez - 4 years, 8 months ago

How can I help

E Koh - 4 years, 8 months ago