Minta tolong jawab dengan caranya ya .. :) 1-2+3-4+5-6+........ +99-100 = ?.... Question from @muhammadhafidz21

October 2018 2 26 Report

Minta tolong jawab dengan caranya ya .. :)
1-2+3-4+5-6+........ +99-100 = ?

dimasrizqi11 (100.49) +50 - 100
4900 - 50
4850
maaf kalau jawabannya salah

0 votes Thanks 1

izharulhaq78 $1-2+3-4+5-6+...+99-100\\(1+3+5+...+99)-(2+4+6+...100)\\\\\diamond1+3+5+...+99\\U_n=2n-1\\99=2n-1\\100=2n\\50=n\\\\\diamond2+4+6+...+100\\U_n=2n\\100=2n\\50=n\\\\\diamond1+3+5+...+99\\S_{n_{ganjil}}=\frac{n}{2}(1+99)\\S_{50}=\frac{50}{2}(100)\\S_{50}=50(50)\\S_{50}=2500\\\\\diamond2+4+6+...+100\\S_{n_{genap}}=\frac{n}{2}(2+100)\\S_{50}=\frac{50}{2}(102)\\S_{50}=50(51)\\S_{50}=2550\\\\1-2+3-4+5-6+...+99-100\\(1+3+5+...+99)-(2+4+6+...100)\\S_{n_{ganjil}}-S_{n_{genap}}\\2500-2550\\\boxed{-50}$

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