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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,459

Hi bobbym,

The solution #1674 is correct. Neat work!

#1675. Find the sum of all natural numbers less than 200 which are divisible by 5.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi ganesh;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,459

Hi bobbym,

The solution #1675 is perfect. Good work!

#1676. Find the sum of all the natural numbers between 200 and 300 which are divisible by 4.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,459

Hi bobbym,

The solution #1676 is perfect. Neat work!

#1677. Find the Arithmetic Progression whose sum to n terms is 2n[sup]2[/sup] + 2. (Find the values of the AP)

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,459

Hi bobbym,

#1678. The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the following it. Find this value of x.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,459

Hi bobbym,

The solution #1678 is correct. Marvelous!

#1679. Find a[sub]30[/sub] - a[sub]20[/sub] for the Arithmetic Progression : a, a + d, a + 2d, a + 3d, ......

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,459

Hi bobbym,

The solution #1679 is correct. Good work!

#1680. Two Arithmetic Progressions have the same common difference. The difference between their 100th term is 111222333. What is the difference between their millionth terms?

Character is who you are when no one is looking.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Hi ganesh

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,459

Hi anonimnystefy and bobbym,

The solution #1680 is correct. Well done!

#1681. Which term of the Arithmetic Progression 21, 18, 15, ..... is 0?

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Hi ganesh

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,459

Hi bobbym and anonimnystefy,

The solution #1681 is correct. Neat work!

#1682. Find the 30th term of the Arithmetic Progression 10, 7, 4, ......

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,459

Hi bobbym,

The solution #1682 is correct. Neat work!

#1683. If a = -18, n = 10, a[sub]n[/sub] = 0, find d.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Hi ganesh

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,459

Hi bobbym and anonimnystefy,

The solution #1683 is perfect. Neat job!

#1684. If a = 3.5, d = 0, n = 105, find a[sub]n[/sub].

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,459

Hi bobbym,

The solution #1684 is correct. Good work!

#1685. Find the number of odd numbers between 0 and 50.

Character is who you are when no one is looking.

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