To express the sum we may write . We can find the exact sum by adding the fractions. One thing that we hope you discover and come to appreciate this semester is that Maple can help you to check your homework. To see how Maple can handle an expression such as this write:

> Sum(1/(i+1),i=1..6);

Now, to evaluate this sum you can change the capital S in Sum to a small s.

> sum(1/(i+1),i=1..6);

Now consider the sum Maple handles this in much the same way, write:

> Sum(j^2,j=n..n+3);

Again, to evaluate this sum you change the capital S in Sum to a small s.

> sum(j^2,j=n..n+3);

Do so. You may not be satisfied with the expression that Maple gives - of course its right but some algebra can clean things up. Use Maple's simplify command to give a simplified expression.

> simplify(%);

Submission:

(a) Use Maple to write the following in summation (Sum) notation, then find the sum for the following:

1. 

2. 

3. + ... +

(b) Find the sum for the following (simplify if necessary).

Submission worksheet:

It is convenient to represent sums using sigma notation when possible. To a large extent this relies on our ability to recognize patterns - a basic mathematical skill that we hope you further develop in this course. To represent 1 + 2 + 4 + 8 + 16 +32 with sigma notation it is important to observe first that each term is a power of 2, starting from the 0th power and ending at the 5th power. So we can write:

> Sum(2^i,i=0..5);

And we can use little s as in Activity 1 to find this sum explicitly.

Submission:

(a) The Maple work showing the explicit value for the sum, 1 + 2 + 4 + 8 + 16 + ... + 1125899906842624.

(b) Use Maple to find the explicit sum +...+ .

Submission worksheet: