100-99+98-97+96-95+...+8-7+6-5+4-3+2-1

Mathematics

2 answers:

lina2011 [118]3 years ago

8 0

$100-99+98-97+96-95+...+8-7+6-5+4-3+2-1\\\\=(100-99)+(98-97)+(96-95)+...+(4-3)+(2-1)\\\\=\underbrace{1+1+1+...+1}_{50}=\fbox{50}$

sergij07 [2.7K]3 years ago

7 0

$x=100-99+98-97+96-95+...+8-7+6-5+4-3+2-1=\\\\=1+1+1+...+1+1+1+1=1\cdot n=n\\\\and\ \ \ 2=100-2\cdot(n-1)\ \ \ \Rightarrow\ \ \ 2n=100\ /:2\ \ \ \Rightarrow\ \ \ n=50\\\\x=50$

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