Sequence and series trivia

[Mohit Pandey]

Hello Hypographites,
Here is a question for all --Find out the total of 1 to 100? Give the method or formula used.

[Erasmus00]

Originally Posted by Mohit Pandey

Hello Hypographites,
Here is a question for all --Find out the total of 1 to 100? Give the method or formula used.

Divide it into 50 pairs of 101. (1+100, 99+2,3+98... etc). Hence, the sum is 50*101= 5050.
-Will

[Qfwfq]

101*50

It can be worked out for the sum of numbers raised to any power but I haven't time to say more right now...

[Mohit Pandey]

Originally Posted by Erasmus00

Divide it into 50 pairs of 101. (1+100, 99+2,3+98... etc). Hence, the sum is 50*101= 5050.
-Will

How did you find out? Any clue.

[ronthepon]

You don't know Arithmetic Progression?

The formula states:



If I still fail to light a bulb,

S: is the sum you want.

a: in the first term of the series

d: 'common difference' is the difference between two succesive numbers in the series.

n: is the number of terms you wish to add in all.

The method Erasmus00 mentioned was first used by Gauss(?), the person who developed the whole concept as a kid.

[Qfwfq]

Of course, in your case Mohit a and d are both 1, so we get n(n + 1)/2. For n = 100 we get 50*101.

Erasmus' post makes it easier to understand why, and you can imagine stacking little squares. Draw one square beside a stack of two and then a stack of three etc. You get half of a big square of little squares, including the diagonal. The big square would be n little squares on each side, try working out exactly how many little squares there are using what Erasmus said.

[BrainForce]

Mohit Pandey haven't u read CBSE X maths .I can do these in a second ,i think u are in IX or VIII otherwise u have known it.
actually they form the basic of A.P (what we call arithmetic progression),a very interesting story of gauss is related with it.

Now my question on sequences -:
a polygon with 100 sides have how many diagnols?

u can use either logic or A.P formulae.


I AM BACK !

[anto]

Originally Posted by ronthepon

You don't know Arithmetic Progression?

The formula states:



.

I think this formula is wrong ronthepon. The formula should be IMO



because the formula for the sum of an arithemtic series is given by (n/2)(t1 +tn) where tn = (t1 + d(n-1)) so I just think you missed an a

I apolagize in advance if im wrong :P

[Mohit Pandey]

Originally Posted by BrainForce

Now my question on sequences -:
a polygon with 100 sides have how many diagnols?

u can use either logic or A.P formulae.

Can anyone help me in solving this question?

[BrainForce]

See,you havew got to find a pattern ,a pattern which is followed by each polygon ,once u get the pattern nothing can deter u from getting this answer.

don't be dependent on formulae,I myself did this question correctly in class VII and used only logic and no formulae.