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...

Quote:

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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...

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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)].