vpasum

Numerically sum the symbolic expression $$\frac{1}{{1.2}^x}$$ from 1 to 1,000.

syms x;
s = vpasum(1/1.2^x,1,1000)

s = $$5.0$$

Find the summation of the symbolic function $$y(x)=x^2$$ from $$a$$ to $$b$$. Since the limits of summation must be real values, assume that the bounds $$a$$ and $$b$$ are real.

syms y(x)
syms a b real
y(x) = x^2;
s = vpasum(y,a,b)

s = 
$${\sum }_{x=a}^b{x}^2$$

Compare the computation time to evaluate symbolic and numerical summations.

Find the symbolic summation of the series $\sum _{\mathit{k}=1}^{\infty }{\left(-1\right)}^{\mathit{k}}\frac{\log \left(\mathit{k}\right)}{{\mathit{k}}^3}$ using symsum. Use vpa to numerically evaluate the symbolic summation using 32 significant digits. Measure the time required to declare the symbolic summation and evaluate its numerical value.

syms k
tic
y = symsum((-1)^k*log(k)/k^3,k,1,Inf)

y = 
$${\sum }_{k=1}^{\infty }\frac{{\left(-1\right)}^k\hspace{0.17em}\log \left(k\right)}{k^3}$$

yVpa = vpa(y)

yVpa = $$0.059705906160195358363429266287926$$

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To increase computation performance (shorten computation time), use vpasum to evaluate the same numerical summation without evaluating the symbolic summation.

tic
y = vpasum((-1)^k*log(k)/k^3,k,1,Inf)

y = $$0.059705906160195358363429266287926$$

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