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Wednesday, March 4, 2009

What is wrong with this equation?

What is wrong with this equation?

1^10 + 2^10 + 3^10.... + 10^10 = ((10*11)/2)^10

Labels: logic

13 Comments:

Anonymous said...: The fact that it is false. But the equation below is true.

1^10 + 2^10 + 3^10.... + 10^10 <> ((10*11)/2)^10; March 4, 2009 2:57 PM
Anonymous said...: The RH term expands to:
(1+2+3+...10)^10
Multiplying this out you get ALL the terms of the LH side PLUS all the cross-multiplication terms.
So the RH side is much greater.; March 4, 2009 3:05 PM
Anonymous said...: Actually if you do the math they are both equal.... 1^10 is 1 to the tenth power which basically is 10so your first number is 10, your next number is 2^10 also as 2 to the tenth power which is 20, next is 3^10 or 3 to the tenth power which is 30, next is 4^10 or 4 to the tenth power which is 40, next is 5^10 or 5 to the tenth power which is 50, next is 6^10 or 6 to the tenth power which is 60, next is 7^10 or 7 to the tenth power which is 70, next is 8^10 or 8 to the tenth power which is 80, next is 9^10 or 9 to the tenth power which is 90, next is 10^10 or 10 to the tenth power which is 100... so now 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 + 100 which equals 550.... the next equation is 10 times 11 which equals 110, then 110 is divided by 2 which equal 55, which is the answer to the first part of the last equation, so the out come is 55^10 or 55 to the tenth power which is also known as 550... so the first and last parts are equal....; March 4, 2009 6:46 PM
Anonymous said...: One to the tenth power is NOT ten.
Your first number is one, not ten.

1^10 = 1

The equation on the left gives 14,914,341,925

The equation on the right is 253,295,162,119,141,000

So they are not equal.; March 4, 2009 8:00 PM
Anonymous said...: I dont get it!

LHS=(1+2+..10)^10
= 55^10

While RHS= (110/2)^10
=55^10

So they are equal.
Right????!!!!
I am confused; March 5, 2009 12:36 AM
Anonymous said...: oh god

lets just look at it in small parts

1^10 + 2^10 is not equal to (1+2)^10 (calculate it if you have any doubts)

So expanding it to 10 terms , clearly lhs is not equal to rhs; March 5, 2009 1:21 AM
Anonymous said...: Clearly

1^10 +
2^10 +
3^10 +
4^10 +
5^10 +
6^10 +
7^10 +
8^10 +
9^10 +
10^10

does not equal 55^10; March 5, 2009 5:10 AM
TdJ said...: I think this is the way to look at it.
Lhs
1^10=1
2^10=1024
3^10=59049
4^10=1048576
5^10=9765625
6^10=60466176
7^10=282475249
8^10=1073741824
9^10=3486784401
10^10=10000000000
------------------+
14914341925

Rhs
55^10= 253295162119140625

Which gives you a small difference. (sarcasm)
This is just because of the simple rule: a^n + b^n is not equal to (a+b)^n

If the equation would have been (1+2+3+4+5+6+7+8+9+10)^10 it would have been equal to ((10*11)/2)^10

Voila.
TdJ; March 5, 2009 8:40 AM
Anonymous said...: seriously, i don't get why there is a "..." in the equation.
but im not that great in math so...best not listen to me!; March 10, 2009 1:45 PM
Anonymous said...: There are two brackets at the start of the answer!!

lol; March 21, 2009 4:12 PM
Anonymous said...: I think OP is correct. The trick is that instead of using ^, it should be *.; March 23, 2009 7:56 PM
Anonymous said...: Sorry, not OP...

The question is, "what is wrong with this?"

And what is wrong is that ^ is used instead of *.; March 23, 2009 7:58 PM
Anonymous said...: whoa! I am 11 years old and I have no idea what this is or how i even got to this website.. How old are you people???? And what does the ^ represent?; June 4, 2009 4:22 PM