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monkeybizz2021trey monkeybizz2021trey
  • 14-08-2014
  • Mathematics
Answered

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

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Anonymous Anonymous
  • 14-08-2014

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

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kate200468
kate200468 kate200468
  • 14-08-2014

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

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