1. ## Sigma Notation

My professor started lecture about integrals with sigma notation...i'm having trouble figuring out how to write the following in sigma notation:

1. 3/5 + 4/6 + 5/7 + 6/8 + 7/9

2. 1-a+a^2-a^3+a^4-a^5+...+(-1)^n a^n

For number one I see the pattern but can't make out the right sum notation.

For number two i got k=0 sigma to n a^k(-1)^k but its wrong I think.

Any help would be great...

2. Originally Posted by swimmergirl
My professor started lecture about integrals with sigma notation...i'm having trouble figuring out how to write the following in sigma notation:

1. 3/5 + 4/6 + 5/7 + 6/8 + 7/9

2. 1-a+a^2-a^3+a^4-a^5+...+(-1)^n a^n

For number one I see the pattern but can't make out the right sum notation.

For number two i got k=0 sigma to n a^k(-1)^k but its wrong I think.

Any help would be great...
Take a look at the first pattern. The denominator is 2 plus the numerator for all terms. Therefore, if the numerator is j, the denominator is j+2. So, the first summations is:

SIGMA_(j=3 to 7)_[j/(j+2)].

The second pattern emphasizes a sign change. This is always achieved with (-1)^n, so that if n is odd, the sign is minus (why?) and if n is even, the sign is plus. The first term is 1, or a^0, so it is convenient to start the summation from zero:

SIGMA_(j=0 to n)_[(-1)^j*(a^j)].