Nilai 1+2⋅2+3⋅22+4⋅23+5⋅24+⋯+2018⋅22017 sama dengan...

Misal soal kita misalkan dengan P.
P=1+2⋅2+3⋅22+4⋅23+⋯+2018⋅22017
ruas kiri dan kanan kita kalikan dengan 2 sehingga kita peroleh;
2P=2+2⋅22+3⋅23+4⋅24+⋯+2018⋅22018

P=1+2⋅2+3⋅22+4⋅23+⋯+2018⋅22017
2P=2+2⋅22+3⋅23+4⋅24+⋯+2018⋅22018 −
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P−2P=1+2+22+23+⋯+22017−2018⋅22018
−P=1+2+22+23+⋯+22017−2018⋅22018
P=2018⋅22018−(1+2+22+23+⋯+22017)
P=2018⋅22018−(22018−1)
P=2018⋅22018−22018+1
P=22018(2018−1)+1
P=22018(2017)+1
P=2017⋅22018+1