Mathematics

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(2¹3¹)/k 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)ⁿ¹) from 1 to ∞

Σ(-1)ⁿ/ln(n) from 2 to ∞

Σ(1+(1/n))ⁿ^² from 1 to ∞

Σ(-1)ⁿ¹/(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)ⁿ¹n!/(1•3•5•…•(2n-1)))+…

Σ(n¹⁰⁰100ⁿ)/n! from 1 to ∞

Σcos(nπ/3)/n! from 1 to ∞

Σ(nπⁿ)/(-3)ⁿ¹ from 1 to ∞

Σ10ⁿ/((n+1)4²ⁿ¹) from 1 to ∞

Σ1/k! from 1 to ∞

Σ(-1)ⁿ¹3ⁿ/(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)ⁿ¹/√n from 1 to ∞

n-th Partial Sum

Series

Σ1/(2n+1) from 1 to ∞

P-Series

Integral Test

∫t⁴lntdt

∫cos¹xdx

∫(x²+2x)cosxdx

∫te³dt

∫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)ⁿ¹e²/ⁿ from 1 to ∞

Σ(-1)ⁿ¹n²/(n³+4) from 1 to ∞

Σ(-1)ⁿeⁿ from 1 to ∞

Σ(-1)ⁿ(3n-1)/(2n+1) from 1 to ∞

Σ(-1)ⁿ¹/(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))²eⁿ 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 ∞

Σ4ⁿ¹/(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 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 ∞

Σn³ 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-e¹/¹ 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) from 1 to ∞

Σ1/(4+eⁿ) from 1 to ∞

Σ3ⁿ¹4ⁿ from 1 to ∞

Σ(2+n)/(1-2n) from 1 to ∞

(1/3)+(1/6)+(1/9)+(1/12)+(1/15)+…

Σe²ⁿ/6ⁿ¹ from 1 to ∞

Σ(-3)ⁿ¹/4ⁿ from 1 to ∞

Σ12(0.73)ⁿ¹ 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

{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}=2ⁿcos(nπ)

{an}=nsin(1/n)

{(cos²n)/2ⁿ}

{n²eⁿ}

{ln(n)/ln(2n)}

{(2n-1)!/(2n+1)!}

{an}=(-1)ⁿ/(2√n)

{an}=n²/√(n³+4n)

{an}=√((1+4n²)/(1+n²))

{an}=e¹/√ⁿ

{an}=3ⁿ7

{an}=(3+5n²)/(n+n²)

{an}=n⁴/(n³-2n)

{an}=(-1)ⁿ¹/5ⁿ

{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 ∞

∫ze²dz 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 ∞

∫edp 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