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Question Number 12267 by tawa last updated on 17/Apr/17

$$\mathrm{Find}\mathrm{the}\mathrm{nth}\mathrm{term}\mathrm{of}\mathrm{the}\mathrm{sequence}$$$$1)\frac{1}{3},\frac{1}{15},\frac{1}{35},\frac{1}{63},\frac{1}{99}$$$$2)\frac{1}{2},\frac{1}{6},\frac{1}{12},\frac{1}{20},\frac{1}{30}$$

Answered by ajfour last updated on 17/Apr/17

$$1)T_n=\frac{1}{4n^2-1}$$$$2)T_n=\frac{1}{n^2+n}$$

Commented by tawa last updated on 17/Apr/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

Answered by Joel576 last updated on 17/Apr/17

$$1)U_1=\frac{1}{3}=\frac{1}{1.3}$$$$U_2=\frac{1}{15}=\frac{1}{3.5}$$$$U_3=\frac{1}{35}=\frac{1}{5.7}$$$$U_n=\frac{1}{(2n-1)(2n+1)}=\frac{1}{4n^2-1}$$$$$$$$2)U_1=\frac{1}{2}=\frac{1}{1.2}$$$$U_2=\frac{1}{6}=\frac{1}{2.3}$$$$U_3=\frac{1}{12}=\frac{1}{3.4}$$$$U_n=\frac{1}{n(n+1)}=\frac{1}{n^2+n}$$

Commented by tawa last updated on 17/Apr/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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