Math Is Fun Forum

Winatte

Member

Registered: 2022-12-29

Posts: 1

Simplifying summation. I am clueless

Hi folks, after researching and studying for the past 2 days on this, I am still unable to find a single darn answer! I feel pretty low because of this, so would appreciate any help you can give.

So this is my question:
Simplify the following summations to the form an3 +
bn2+cn. Give values for a, b and c for each question.

1.

2.

3.

4.

I know the answers to the first three can be built up from these:

 

But I have no clue actually how to get the answers, as I was only taught and shown how to use set formulas on a given sum, so for instance

  would be n(n+1) over 2.

I am stuck!
Even a link to a website which could help me understand this question a bit better would be much appreciated.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,618

Re: Simplifying summation. I am clueless

hi Winatte

Welcome to the forum.

The formula for the sum of squares ( 1 + 4 + 9 + 16 + ... + n^2) is

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

Substitute n = 1, 2, 3 etc to show that it works.

There are also similar formulas for the sum of cubes and higher powers but they get increasingly complicated.

Q1 is just 5 + 5 + 5 + 5 ... 'n' times = 5n.  I don't understand what " an3 + bn2 + cn" means for this.

We can make more progress with this over several posts so please reply.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob