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vish22
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Yo guys,I was wondering if there was an easy logical way of finding a general n-th term in a sequence of partial sums for any converging sequence {a-n}
vish22 said:Yo guys,I was wondering if there was an easy logical way of finding a general n-th term in a sequence of partial sums for any converging sequence {a-n}
A general term in partial sum refers to a mathematical expression that represents the nth term in a sequence of numbers that are being added together to form a sum. It is used to determine the value of a partial sum, which is the sum of a specific number of terms in the sequence.
The general term in partial sum can be calculated using the formula: an = a1 + (n-1)d, where an represents the nth term, a1 is the first term, and d is the common difference between consecutive terms in the sequence.
Finding the general term in partial sum is useful in determining the value of a specific term in a sequence, without having to add all the terms before it. It also allows for the prediction of future terms in the sequence.
One example is calculating the sum of the first n natural numbers, where the general term in partial sum would be n(n+1)/2. Another example is finding the sum of a geometric sequence, where the general term in partial sum would be a(1-rn)/(1-r), with a representing the first term and r being the common ratio.
Yes, the general term in partial sum can be used for infinite series. In this case, the formula is an = a1 + (n-1)d, where d is the common difference between consecutive terms in the series. However, the series must be convergent for this formula to be applicable.