Sum of Consecutive Odds, Evens, Squares, etc...

[mtamassia]

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]

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

[iisan]

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]

Thanks for the post.

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

[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!

[coolsrini1981]

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