Generating functions for given sequences

Task number: 3868

Construct generating functions for the following sequences. Do not use infinite series in the result:

  • Variant

    \((1{,}1,1{,}1,1{,}1,\ldots)\)

  • Variant

    \((1,-1{,}1,-1{,}1,-1,\ldots)\)

  • Variant

    \((1{,}0,1{,}0,1{,}0,\ldots)\)

  • Variant

    \((1{,}2,3{,}4,5{,}6,\ldots)\)

  • Variant

    \((1,-1{,}2,-2{,}3,-3{,}4,-4,\ldots)\)

  • Variant

    \((2{,}1,4{,}3,6{,}5,\ldots)\)

  • Variant

    \((1{,}2,1{,}4,1{,}8,\ldots)\)

  • Variant

    \((1,-3{,}5,-7{,}9,-11,\ldots)\)

  • Variant

    \((0{,}1,1{,}2,2{,}4,3{,}8,4{,}16,\ldots,i,2^i,\ldots)\)

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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