Solving Problems in Differential Calculus |
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Page 73
... series is a series of positive terms . Since Sn + 1 = Sn + un + 1 , S , is an increasing function of n , so that as n → ∞ , Scannot oscillate or tend to ∞ . It either converges to a positive sum S , or it diverges to + ∞ . THEOREM 1 ...
... series is a series of positive terms . Since Sn + 1 = Sn + un + 1 , S , is an increasing function of n , so that as n → ∞ , Scannot oscillate or tend to ∞ . It either converges to a positive sum S , or it diverges to + ∞ . THEOREM 1 ...
Page 74
... series being a term in the other , though perhaps in a different posi- tion in the series , then Σ v , converges to S. This theorem is not true about a conditionally convergent series . If Σ un converges to S , and Σ v , converges to T , ...
... series being a term in the other , though perhaps in a different posi- tion in the series , then Σ v , converges to S. This theorem is not true about a conditionally convergent series . If Σ un converges to S , and Σ v , converges to T , ...
Page 82
... convergent to sum a 。 when x = 0 . If it is convergent for no other value of x we say that its radius of convergence is zero . If the series is convergent for all values of x we say that its radius of convergence is infinite . In any ...
... convergent to sum a 。 when x = 0 . If it is convergent for no other value of x we say that its radius of convergence is zero . If the series is convergent for all values of x we say that its radius of convergence is infinite . In any ...
Common terms and phrases
1+x² 2x sin 3x absolutely convergent ADDITIONAL EXAMPLES angle approximately Binomial series conditionally convergent constant cos² 5x cos³ cosec cosh cosh x cosh2 coth curve d²y dx2 d²y dy d²y/dx² decimal places Deduce derivative Differentiate dt dt dx dt dx dy dx2 dx dy dx dy/dx equation feet Find the stationary finite limit harmonic series Hence hyperbolic functions increases J₁ Leibnitz's Theorem logarithm Maclaurin expansion Maclaurin series maximum minimum n²)n nt+a oscillates finitely polynomial positive integer positive terms power series power series expansion prove radians radius of convergence sec² sec³ sech series diverges series is convergent sin x sin¯¹ sin¹ sin² sin³ sinh sinh2 Sketch the graph SPDC stationary points tangent tends to infinity term in x4 u₁ velocity x-sin x+cos x²+1 y₁ Ип