A worker is paid 0.05 on the first day, 0.10 on the second day, 0.20 on the third day and 0.40 on the fourth day, and so on. How much money in total does the work earn after working 21 days?
A worker is paid 0.05 on the first day, 0.10 on the second day, 0.20 on the third day and 0.40 on the fourth day, and so on. How much money in total does the work earn after working 21 days?
after 1 day :0.05after 2 days :0.10=0.05⋅2after 3 days :0.20=0.10⋅2=0.05⋅2⋅2=0.05⋅22after 4 days :0.40=0.20⋅2=0.05⋅22⋅2⋅2=0.05⋅23…after 21 days :0.05⋅221−1=0.05⋅220=0.05⋅1048576=52428.80
He earn after 21 days 52428.80
A worker is paid 0.05 on the first day, 0.10 on the second day, 0.20 on the third day and 0.40 on the fourth day, and so on. How much money in total does the work earn after working 21 days?
after 1 day :0.05after 2 days :0.10=0.05⋅2after 3 days :0.20=0.10⋅2=0.05⋅2⋅2=0.05⋅22after 4 days :0.40=0.20⋅2=0.05⋅22⋅2⋅2=0.05⋅23…after 21 days :0.05⋅221−1=0.05⋅220=0.05⋅1048576=52428.80
all days together:
geometric sequence
a1=0.05
r=2
s=a1(1−r211−r)s=a1(r21−1r−1)s=0.05(221−12−1)s=0.05(221−11)s=0.05⋅221s=0.05⋅2097152s=104857.60
A worker is paid 0.05 on the first day, 0.10 on the second day, 0.20 on the third day and 0.40 on the fourth day, and so on. How much money in total does the work earn after working 21 days?
without mistake:
all days together:
geometric sequence
a1=0.05
r=2
s=a1(1−r211−r)s=a1(r21−1r−1)s=0.05(221−12−1)s=0.05(221−11)s=0.05⋅(221−1)s=0.05⋅2097151s=104857.55