Whakaoti i te 1/n-1/n+1

$$\frac { 1 } { n } - \frac { 1 } { n + 1 }$$

Aromātai

$$\frac{1}{n\left(n+1\right)}$$

Ngā Hipanga Rongoā Poto

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o n me n+1 ko n\left(n+1\right). Whakareatia \frac{1}{n} ki te \frac{n+1}{n+1}. Whakareatia \frac{1}{n+1} ki te \frac{n}{n}.

$$\frac{n+1}{n\left(n+1\right)}-\frac{n}{n\left(n+1\right)}$$

Tā te mea he rite te tauraro o \frac{n+1}{n\left(n+1\right)} me \frac{n}{n\left(n+1\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{n+1-n}{n\left(n+1\right)}$$

Whakakotahitia ngā kupu rite i n+1-n.

$$\frac{1}{n\left(n+1\right)}$$

Whakarohaina te n\left(n+1\right).

$$\frac{1}{n^{2}+n}$$

Kimi Pārōnaki e ai ki n

$$-\frac{2n+1}{\left(n\left(n+1\right)\right)^{2}}$$

Ngā Upane e Whakamahi ana i te Ture Mekameka

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o n me n+1 ko n\left(n+1\right). Whakareatia \frac{1}{n} ki te \frac{n+1}{n+1}. Whakareatia \frac{1}{n+1} ki te \frac{n}{n}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{n+1}{n\left(n+1\right)}-\frac{n}{n\left(n+1\right)})$$

Tā te mea he rite te tauraro o \frac{n+1}{n\left(n+1\right)} me \frac{n}{n\left(n+1\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{n+1-n}{n\left(n+1\right)})$$

Whakakotahitia ngā kupu rite i n+1-n.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{n\left(n+1\right)})$$

Whakamahia te āhuatanga tohatoha hei whakarea te n ki te n+1.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{n^{2}+n})$$

Mēnā ko F te hanganga o ngā pānga e rua e taea ana te pārōnaki f\left(u\right) me u=g\left(x\right), arā, mēnā ko F\left(x\right)=f\left(g\left(x\right)\right), ko te pārōnaki o F te pārōnaki o f e ai ki u whakareatia te pārōnaki o g e ai ki x, arā, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$-\left(n^{2}+n^{1}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}n}(n^{2}+n^{1})$$

Ko te pārōnaki o tētahi pūrau ko te tapeke o ngā pārōnaki o ōna kīanga tau. Ko te pārōnaki o tētahi kīanga tau pūmau ko 0. Ko te pārōnaki o te ax^{n} ko te nax^{n-1}.

$$-\left(n^{2}+n^{1}\right)^{-2}\left(2n^{2-1}+n^{1-1}\right)$$

Whakarūnātia.

$$\left(n^{2}+n^{1}\right)^{-2}\left(-2n^{1}-n^{0}\right)$$

Mō tētahi kupu t, t^{1}=t.

$$\left(n^{2}+n\right)^{-2}\left(-2n-n^{0}\right)$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\left(n^{2}+n\right)^{-2}\left(-2n-1\right)$$