Multiplying Power Series
{1,-4/2,9/6,-16/24,25/120,…}
{1/3,5/9,9/27,13/81,…}
Maclaurin Series f(x)=(1-x)⁻²
Power Series f(x)=2/(3-x)
Taylor Series f(x)=xeˣ, a=0
Power Series f(x)=1/(1+x)
Σn!/eⁿ^² from 1 to ∞
Σtan(1/n) from 1 to ∞
Σ(-1)ⁿcos(1/n²) from 1 to ∞
Σ(-1)ⁿ(ln(n)/√n) from 1 to ∞
Σ(1•3•5•…•(2n-1))/(2•5•8•…•(3n-1)) from 1 to ∞
Σ(2ᵏ⁻¹3ᵏ⁺¹)/kᵏ from 1 to ∞
Σ(3ⁿn²)/n! from 1 to ∞
Σ(1/n³)+(1/3ⁿ) from 1 to ∞
Σ(-1)ⁿπ²ⁿ/(2n)! from 0 to ∞
Σ1/(n√ln(n)) from 2 to ∞
Σeⁿ/n² from 1 to ∞
Σ(-1)ⁿ(n²-1)/(n³+1) from 1 to ∞
Σ(n²-1)/(n³+1) from 1 to ∞
Σ((-1)ⁿarctan(n))/n² from 1 to ∞
Σ(n/ln(n))ⁿ from 2 to ∞
Σ(-9)ⁿ/(n(10)ⁿ⁺¹) from 1 to ∞
Σ(-1)ⁿ/ln(n) from 2 to ∞
Σ(1+(1/n))ⁿ^² from 1 to ∞
Σ(-1)ⁿ⁻¹/(ln(n))ⁿ from 2 to ∞
Σ((n²+1)/(2n²+1))ⁿ from 1 to ∞
Σ(2•4•6•…•2n)/n! from 1 to ∞
1-(2!/(1•3))+(3!/(1•3•5))-(4!/(1•3•5•7)+…+((-1)ⁿ⁻¹n!/(1•3•5•…•(2n-1)))+…
Σ(n¹⁰⁰100ⁿ)/n! from 1 to ∞
Σcos(nπ/3)/n! from 1 to ∞
Σ(nπⁿ)/(-3)ⁿ⁻¹ from 1 to ∞
Σ10ⁿ/((n+1)4²ⁿ⁺¹) from 1 to ∞
Σ1/k! from 1 to ∞
Σ(-1)ⁿ⁻¹3ⁿ/(2ⁿn³) from 1 to ∞
Σn/5ⁿ from 1 to ∞
Σsin(n)/2ⁿ from 1 to ∞
Σ(-1)ⁿ/(n³+1) from 1 to ∞
Σ(-1)ⁿ/(5n+1) from 0 to ∞
Σ(-1)ⁿ⁻¹/√n from 1 to ∞
n-th Partial Sum
Series
Σ1/(2n+1) from 1 to ∞
P-Series
Integral Test
∫t⁴lntdt
∫cos⁻¹xdx
∫(x²+2x)cosxdx
∫te⁻³ᵗdt
∫xcos5xdx
Σ(-1)ⁿnⁿ/n! from 1 to ∞
Σ(-1)ⁿsin(π/n) from 1 to ∞
Σsin((n+(1/2))π)/(1+√n) from 0 to ∞
Σ(-1)ⁿ⁻¹e²/ⁿ from 1 to ∞
Σ(-1)ⁿ⁺¹n²/(n³+4) from 1 to ∞
Σ(-1)ⁿe⁻ⁿ from 1 to ∞
Σ(-1)ⁿ(3n-1)/(2n+1) from 1 to ∞
Σ(-1)ⁿ⁻¹/(3+5n) from 1 to ∞
(-2/5)+(4/6)-(6/7)+(8/8)-(10/9)+…
Σsin(1/n) from 1 to ∞
Σ1/n! from 1 to ∞
Σ(1+(1/n))²e⁻ⁿ from 1 to ∞
Σ(eⁿ+1)/(neⁿ+1) from 1 to ∞
Σ(5+2n)/(1+n²)² from 1 to ∞
Σ√(n+1)/(2+n) from 1 to ∞
Σ(n+1)/(n³+n) from 1 to ∞
Σ1/√(n²+1) from 1 to ∞
Σ4ⁿ⁺¹/(3ⁿ-2) from 1 to ∞
Σ(1+cos(n))/eⁿ from 1 to ∞
Σ³√k/(√(k³+4k+3)) from 1 to ∞
Σln(k)/k from 1 to ∞
Σ9ⁿ/(3+10ⁿ) from 1 to ∞
Σ(n+1)/(n√n) from 1 to ∞
Σ1/(n³+8) from 1 to ∞
Σn/(n⁴+1) from 1 to ∞
Σ(cosπn)/√n from 1 to ∞
Σ1/(n²+n³) from 1 to ∞
Σke⁻ᵏ from 1 to ∞
Σ1/(nln(n)) from 1 to ∞
Σn³/(n⁴+4) from 1 to ∞
Σ1/(n²+4) from 1 to ∞
Σ(√n+4)/n² from 1 to ∞
(1/3)+(1/7)+(1/11)+(1/15)+(1/19)+…
1+(1/8)+(1/27)+(1/64)+(1/125)+…
Σ1/n^√² from 1 to ∞
Σn/(n²+1) from 1 to ∞
Σ2/(5n-1) from 1 to ∞
Σn⁻³ from 1 to ∞
Σ(-5)ⁿxⁿ from 1 to ∞
Σ(x-2)ⁿ/3ⁿ from 0 to ∞
1.234467567567…
2.516516516…
0.8888…
Σe¹/ⁿ-e¹/⁽ⁿ⁺¹⁾ from 1 to ∞
Σ3/(n(n+3)) from 1 to ∞
Σ2/(n²-1) from 2 to ∞
Σ(1/eⁿ)+(1/(n(n+1)) from 1 to ∞
Σ(sin100)ᵏ from 1 to ∞
Σ1/(4+e⁻ⁿ) from 1 to ∞
Σ3ⁿ⁺¹4⁻ⁿ from 1 to ∞
Σ(2+n)/(1-2n) from 1 to ∞
(1/3)+(1/6)+(1/9)+(1/12)+(1/15)+…
Σe²ⁿ/6ⁿ⁻¹ from 1 to ∞
Σ(-3)ⁿ⁻¹/4ⁿ from 1 to ∞
Σ12(0.73)ⁿ⁻¹ from 1 to ∞
3-4+(16/3)-(64/9)+…
10-2+0.4-0.08+…
Comparing Series
{an}=2n/(3n+1)
{sin(n)}
Σ1/(n⁴+n²) from 1 to ∞
Σsin(n) from 1 to ∞
{an}=3-2ne⁻ⁿ
{an}=n(-1)ⁿ
{an}=(1-n)/(2+n)
{an}=1/(2n+3)
{an}=arctan(ln(n))
{an}=ln(2n²+1)-ln(n²+1)
{an}=(1+(2/n))ⁿ
{an}=2⁻ⁿcos(nπ)
{an}=nsin(1/n)
{(cos²n)/2ⁿ}
{n²e⁻ⁿ}
{ln(n)/ln(2n)}
{(2n-1)!/(2n+1)!}
{an}=(-1)ⁿ/(2√n)
{an}=n²/√(n³+4n)
{an}=√((1+4n²)/(1+n²))
{an}=e⁻¹/√ⁿ
{an}=3ⁿ7⁻ⁿ
{an}=(3+5n²)/(n+n²)
{an}=n⁴/(n³-2n)
{an}=(-1)ⁿ⁻¹/5ⁿ
{1/2,-4/3,9/4,-16/5,25/6…}
{-3,2,-4/3,8/9,-16/27,…}
{5,8,11,14,17,…}
{4,-1,1/4,-1/16,1/64…}
{1/2,1/4,1/6,1/8,1/10,…}
{a1}=2, {an+1}={an}/(1+{an})
{a1}=1, {an+1}=5{an}-3
sequence = 1/(n+1)!
sequence = 2ⁿ/(2n+1)
∫z/z⁴+4dz from -∞ to 0
∫ln(x)/xdx from 1 to ∞
∫ze²ᶻdz from -∞ to 0
∫1/(x²+x)dx from 1 to ∞
∫sin²αdα from 0 to ∞
∫xe ⁻ˣ^²dx from -∞ to ∞
∫x²/√(1+x³)dx from 0 to ∞
∫e⁻⁵ᵖdp from 2 to ∞
∫1/(3-4x)dx from -∞ to 0
∫1/((x-2)³/²)dx from 3 to ∞
∫1/(x²√(x²+4))dx
Strategy for Integration
∫ln(x²+9)dx
∫1/(1+eˣ)dx
∫1/(1-cosx)dx
∫√(x²-9)/x²dx
∫√(9-25x²)dx
∫1/(x²+3)³/²dx
∫x²√(5-x³)dx
GOD OF MATH
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