Expert: David Hemmer - 6/11/2007

Question

I have a math portfolio due in a few days and the teacher's like this is going to be our final draft and he's not gonna give us any extras...
and...i have no idea how to solve the probs...he wont answer any questions...so im gonna have to ask you..

Its really urgent please help..

1. For the infinite sequence (an), where a1 = 1*2; a2 = 2*3; a3 = 3*4 ..... to infinity find an expression for an , the nth term (general term) of the seuqnce

Ok its obviously n(n+1) but how do i proove it.

and one more question pleasee

2. Consider the series Sn= a1+a2+a3+...+an, where ak is defined as above (n(n+1))
Determine the first 6 values of Sk and note your observations.. i foudn the values.. but coudnt find any patterns or observations as such
Formulate a conjecture for the general expression of Sn...(wahhhhhhh???)
Prove you conjecture by induction (double wahhh???)
Using hte result above, calculate 1^2+2^2+....n^2

so in short HELPPPPPPPPPPPPPPPPPPPPPPPPPPPP
I need it as soona s possible

please replyyyyyyyyyy

Answer
1. Your answer is right, there is nothing to prove. You are just giving a formula that matches the sequence.

2.  I don't see how you are going to see a pattern here. What you are calculating is the

Sum_i=1 to n of i^2+i.

There is a formula for the sum of the first n positive integers and the first n squares. I suggest you look

http://web01.shu.edu/projects/reals/infinity/answers/sm_sq_cb.html

for everything you need.