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mtamassia · 2006 July 6th, 07:07 PM

Hi Folks,

I keep wasting a long time with questions asking about Sum consecutive numbers. I try not to memorize the formulas but sometimes it can take some time just to get it.

I found different approaches on different posts so I wanted to consolidate it on this post.

1) The Sum of Consecutive Numbers

I just average the First and Last, and multiply the result by the number of numbers on the range (adding 1, if inclusive). Is there an easier/better way?

2) The Sum of Consecutive Positive Evens

???

3) The Sum of Consecutive Positive Odds

???

4) The Sum of Consecutive Squares

???

thegoat · 2006 July 7th, 05:35 PM

the easiest way would be 2 use the knowledge of progressions...

iisan · 2006 July 8th, 01:50 AM

1) The Sum of Consecutive Numbers

n(n+1)/2

2) The Sum of Consecutive Positive Evens

n(n+1)

3) The Sum of Consecutive Positive Odds

n^2

4) The Sum of Consecutive Squares

n(n+1)(2n+1)/6

mtamassia · 2006 July 8th, 09:58 PM

Thanks for the post.

Now we only need the Sum of Consecutive Reciprocals...

tejpret · 2006 July 15th, 06:15 PM

Sum of 1st N integer numbers starting from 1
n(n+1)
2

Sum of 1st N^2 integer numbers starting from 1
n(n+1)(2n+1)

6

Sum of 1st N^3 integer numbers starting from 1
(1 n(n+1))^2
2

N people making handshake that every shakes hand with every other person
n(n-1)
2

For Reciprocal I have the following
1 + 1 + 1 + ..........+ 1
201 202 203 300

Find Range
1 * 100 = 1 (approx)
201 2

1 * 100 = 1 (approx)
300 3

So answere should be between 1 & 1
2 3

Hope it helps!

coolsrini1981 · 2006 July 24th, 03:42 AM

Quote:

Originally Posted by tejpret

Sum of 1st N integer numbers starting from 1
n(n+1)
2

Sum of 1st N^2 integer numbers starting from 1
n(n+1)(2n+1)

6

Sum of 1st N^3 integer numbers starting from 1
(1 n(n+1))^2
2

N people making handshake that every shakes hand with every other person
n(n-1)
2

For Reciprocal I have the following
1 + 1 + 1 + ..........+ 1
201 202 203 300

Find Range
1 * 100 = 1 (approx)
201 2

1 * 100 = 1 (approx)
300 3

So answere should be between 1 & 1
2 3

Hope it helps!

Excellent one tejpreet..can u pls elaborate the reciprocals part mentioned..i could not getit..thks in adv

2006 July 6th, 07:07 PM	#1 (permalink)
mtamassia I JUST got here. Join Date: Jun 2006 Posts: 13	Sum of Consecutive Odds, Evens, Squares, etc... Hi Folks, I keep wasting a long time with questions asking about Sum consecutive numbers. I try not to memorize the formulas but sometimes it can take some time just to get it. I found different approaches on different posts so I wanted to consolidate it on this post. 1) The Sum of Consecutive Numbers I just average the First and Last, and multiply the result by the number of numbers on the range (adding 1, if inclusive). Is there an easier/better way? 2) The Sum of Consecutive Positive Evens ??? 3) The Sum of Consecutive Positive Odds ??? 4) The Sum of Consecutive Squares ???

2006 July 7th, 05:35 PM	#2 (permalink)
thegoat Eager! Join Date: Jun 2006 Location: India Posts: 90	the easiest way would be 2 use the knowledge of progressions... _ _ _ _ SIG _ _ _ _ The Greatest Of All Times

2006 July 8th, 01:50 AM	#3 (permalink)
iisan Within my grasp! Join Date: Apr 2006 Posts: 348	1) The Sum of Consecutive Numbers n(n+1)/2 2) The Sum of Consecutive Positive Evens n(n+1) 3) The Sum of Consecutive Positive Odds n^2 4) The Sum of Consecutive Squares n(n+1)(2n+1)/6 _ _ _ _ SIG _ _ _ _ Some people are more talented than others. Some are more educationally privileged than others. But we all have the capacity to be great. Greatness comes with recognizing that your potential is limited only by how you choose, how you use your freedom, how resolute you are, how persistent you are -- in short, by your attitude. And we are all free to choose our attitude. -- Peter Koestenbaum

2006 July 15th, 06:15 PM	#5 (permalink)
tejpret Eager! Join Date: Jan 2005 Location: New Delhi, India Posts: 30	I have something to add Sum of 1st N integer numbers starting from 1 n(n+1) 2 Sum of 1st N^2 integer numbers starting from 1 n(n+1)(2n+1) 6 Sum of 1st N^3 integer numbers starting from 1 (1 n(n+1))^2 2 N people making handshake that every shakes hand with every other person n(n-1) 2 For Reciprocal I have the following 1 + 1 + 1 + ..........+ 1 201 202 203 300 Find Range 1 * 100 = 1 (approx) 201 2 1 * 100 = 1 (approx) 300 3 So answere should be between 1 & 1 2 3 Hope it helps!

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2006 July 8th, 09:58 PM	#4 (permalink)
mtamassia I JUST got here. Join Date: Jun 2006 Posts: 13	Thanks for the post. Now we only need the Sum of Consecutive Reciprocals...

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