Sum of a series?

I'm having some trouble even finding somewhere to start with these problems, where I have to find the sum of these without using for loops:

1) 1/(1*2) + 1/(2*3)+ 1/(3*4)+ 1/(4*5)+....1/(99*100)

2) e^1-e^2+e^3-e^4....+e^99-e^100

3) x+ x^2/2 + x^3/3 + x^4/4 +.... x^10/10 for x = 0.5

Answer 1

[Matt J]

Hint:

>> 1./(1:5)

ans =

    1.0000    0.5000    0.3333    0.2500    0.2000

[John Mitchell]

How do I then use this for the exponentially growing denominator? It doesn't increases lineraly, but instead by 2, then 4, then 6 etc.

[Matt J]

Think of the variety of things that you can do with this concept, e.g.,

>> x=1:5;
>> 1./(x.*(x+2).^2)

ans =

    0.1111    0.0313    0.0133    0.0069    0.0041

[John Mitchell]

Thank you so much! I got the first one to work now, and I think I have a idea of how to do the third one, but I am still clueless on how to do the changing signs of the second one

[Matt J]

The second one is a geometric series with ratio r=-exp(1). It has a closed form formula.