IIT JEE , AIEEE Forum - Mathematics , Algebra

spideyunlimited

a gentleman deposites one paise in a bank on the first of march . in the subsequent days he deposits two paise more than his balance with the bank till the previous day . what will be his balance at the end of the month

he deposits...
1 then (1+2)
then 1 + (1+2) + 2. .. and so on

So he deposits (starting from day 1) :
1
3
6
12
24
48
96
....
and so on
as you can see after the first day, it is a GP with r = 2
..

Considering the month to be 30 days :
total balance at end of month =
1 + (3 + 3*2 + 3*2*2 + 3*2*2*2 ..... 3*2*2... with 28 2s)
= 1 + 3*(2^29 - 1) / (2 - 1)

= 1 + 3(536870912 - 1) / 1
= 1 + 3 (536870911)
= 1 + 1610612733 = 1610612734

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