Olympiad workbookIOQMSequences and Series

What is the value of _ 1 i < j 10 i+j= odd (i+j)- _ 1 i < j 10 i+j= even (i+j) ?

Correct answer

Step-by-step solution

Sum of odd = 3+5+7+9+ +19 ₉+ 5+7+ +17 ₇+ 7+9+ +15 ₅+ 9+11+13 ₃+11 Sum of even = 4+6+ +18 ₈+ 6+8+ +16 ₆+ 8+10+12+14 ₄+ 10+12 ₂ Difference =(-1-1-1 .8 times )+19+(-1-1-1 .6 times )+17+(-1-1-1-1)+15+(-1-1)+13+11=-8-6-4-2+19+17+15+13+11=75-20=55

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