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Examples for

Sums

Summation is the addition of a list, or sequence, of numbers. If the summation sequence contains an infinite number of terms, this is called a series. Sums and series are iterative operations that provide many useful and interesting results in the field of mathematics.

Finite Sums

Compute a finite summation of a mathematical expression.

Compute an indexed sum:

sum j^2, j=1 to 100

sum x^k, k=0 to n

Start Summation, Start index of summation, i , index of summation End,Start lower bound, 1 , lower bound End,Start upper bound, 10 , upper bound End,Start expression, Start Fraction, Start numerator, 1 , numerator End,Start denominator, Start Power, Start base, 2 , base End,Start exponent, i , exponent End , Power End , denominator End , Fraction End , expression End , Summation End10i=112i

Sum an incompletely specified sequence of terms:

3+12+27+...+300

Start Power, Start base, 1 , base End,Start exponent, 2 , exponent End , Power End + Start Power, Start base, 2 , base End,Start exponent, 2 , exponent End , Power End + Start Power, Start base, 3 , base End,Start exponent, 2 , exponent End , Power End + ... + Start Power, Start base, 10 , base End,Start exponent, 2 , exponent End , Power End12+22+32+ ... +102

Sum Convergence

Explore the behavior of series, in particular whether or not they converge to a particular value.

Determine if an infinite sum converges:

sum convergence of n

sum convergence of n^(-2)

does the sum of 2^(-n) converge

does the sum of 5*3^(1 - n) converge

Infinite Sums

Find the sum of an infinite number of terms.

Compute an infinite sum:

sum 1/n^2, n=1 to infinity

sum x^k/k!, k=0 to +oo

Start Summation, Start index of summation, i , index of summation End,Start lower bound, 3 , lower bound End,Start upper bound, ∞ , upper bound End,Start expression, Start Fraction, Start numerator, Start Power, Start base, (-1) , base End,Start exponent, i , exponent End , Power End , numerator End,Start denominator, Start Power, Start base, (i - 2) , base End,Start exponent, 2 , exponent End , Power End , denominator End , Fraction End , expression End , Summation End∞i=3-1ii - 22

Sum a geometric series:

sum (3/4)^j, j=0..infinity

sum x^n, n=0 to +oo

Compute a sum over all integers:

sum 1/(1+n^2), n=-oo to +oo

Compute an infinite sum (limits unspecified):

Sum an incompletely specified infinite series:

1/2 + 1/4 + 1/8 + 1/16 + ...

1/2^2 + 1/3^2 + 1/5^2 + 1/7^2 + ...

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Step-by-Step Solutions for Calculus

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