What is the sum of the digits of the decimal form of the product below?
1999 2001
2 x 5
What is the sum of the digits of the decimal form of the product below?
1999 2001
2 x 5
Hi,
Your problem is not clear. what you want actually? what is the meaning of the following...
1999 2001
2 x 5
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suresh
I think you need the solution for the following....
(2^1999 * 5^2001) Sum of the results of this product...
Am i correct?
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suresh
Yes. You R Correct
The answer for your problem is 7.
Solution:
Your problem is (2^n * 5^(n+2))
Let's take n=1
result is 2*125 = 250 = 7
Let's take n=2
result is 4*625 = 2500 = 7
Let's take n=3
result is 8*3125 = 25000 = 7
Let's take n=4
result is 16*15625 = 250000 = 7
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.
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So finally we got the result like 250...... and the sum is 7
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suresh
That's a Great Logic!
Thnks.
2^n*5^(n+2)
= 2^n*5^n*5^2
=(2*5)^n*25
=10^n*25
Sum is always 7.
great thinking suresh..
2^1999=(2^2000)/2
5^2001=(5^2000)*5
lhs={(2*5)^2000}*5/2=(10^2)^1000*2.5=(100^1000)*2.5=(1 followed by 20 zeroes)*2.5=25 followed by 19 zeroes=>this gives sum of digits=2+5=7
2^1999=(2^2000)/2
5^2001=(5^2000)*5
lhs={(2*5)^2000}*5/2
(10^2000)*2.5
{(10^2)^1000}*2.5
(100^1000)*2.5
(1 followed by 20 zeroes)*2.5
25 followed by 19 zeroes
hence, sum of digits =2+5=7
just getting the advantage of particular set of 2 & 5