+0

0
167
5
+2765

$$\dfrac{2027!+2028!}{2028!-2029!}$$

tertre  Mar 6, 2017

#3
+92805
+5

Hi Tetre :)

$$\dfrac{2027!+2028!}{2028!-2029!}\\ =\dfrac{2027!+2027!*2028}{2028!-2028!*2029}\\ =\dfrac{2027!(1+2028)}{2028!(1-2029)}\\ =\dfrac{2027!(2029)}{2028!(-2028)}\\ =\dfrac{(2029)}{2028(-2028)}\\ =\dfrac{-2029}{2028^2}\\$$

-2029/(2028*2028) = -0.000493339791246

Melody  Mar 6, 2017
#1
+3
0

-4055

jroozeboom  Mar 6, 2017
#2
+87309
+5

[ 2027! + 2028!]  / [ 2028! - 2029! ]

Note that we can write this as

[ (2027!) (1 + 2028) ]  / [ (2027!) ( 2028 - 2028*2029) ] =

(1 + 2028) / [ 2028 ( 1 - 2029)]

(2029) / [ 2028 (-2028)] =

-(2029) / 2028^2  =

-2029 / 4,112,784

CPhill  Mar 6, 2017
#3
+92805
+5

Hi Tetre :)

$$\dfrac{2027!+2028!}{2028!-2029!}\\ =\dfrac{2027!+2027!*2028}{2028!-2028!*2029}\\ =\dfrac{2027!(1+2028)}{2028!(1-2029)}\\ =\dfrac{2027!(2029)}{2028!(-2028)}\\ =\dfrac{(2029)}{2028(-2028)}\\ =\dfrac{-2029}{2028^2}\\$$

-2029/(2028*2028) = -0.000493339791246

Melody  Mar 6, 2017
#4
+19653
0

$$\dfrac{2027!+2028!}{2028!-2029!}$$

$$\begin{array}{|rcll|} \hline && \dfrac{2027!+2028!}{2028!-2029!} \\\\ &=& \dfrac {\frac{2028!}{2028} +2028!} {2028!-2028!\cdot 2029} \\\\ &=& \dfrac { 2028!\cdot \left( \frac{1}{2028} + 1\right) } { 2028!\cdot (1-2029) } \\\\ &=& \dfrac { \frac{1}{2028} + 1} { 1-2029 } \\\\ &=& \dfrac { \frac{1}{2028} + 1} { -2028 } \\\\ &=& \dfrac { 1+2028 } { -2028^2 } \\\\ &=& -\dfrac { 2029 } { 2028^2 } \\\\ \hline \end{array}$$

heureka  Mar 6, 2017
#5
0

(2027! + 2028!)/(2028! - 2029!) = (2026!! 2027!! + 2027!! 2028!!) / (2027!! 2028!! - 2028!! 2029!!), where !! = Double factorial. OR: (2027! + 2028!)/(2028! - 2029!) = (Γ(2028) + Γ(2029))/(Γ(2029) - Γ(2030)), where Γ = The Gamma function.

Guest Mar 6, 2017