Question

# Find the nth term of the sequence$$\dfrac{1}{2}, \dfrac{2}{3}, \dfrac{3}{4}, ..........$$

Solution

## In the given sequence is $$\cfrac { 1 }{ 2 } ,\cfrac { 2 }{ 3 } ,\cfrac { 3 }{ 4 } ,......$$, the first term $$t_{ 1 }=\cfrac { 1 }{ 2 }$$, second term $$t_{ 2 }=\cfrac { 2 }{ 3 }$$ and third term $$t_{ 3 }=\cfrac { 3 }{ 4 }$$. We observe that:$$t_{ 1 }=\cfrac { 1 }{ 1+1 } =\cfrac { 1 }{ 2 }$$ and $$t_{ 2 }=\cfrac { 2 }{ 2+1 } =\cfrac { 2 }{ 3 }$$ and so on...Therefore, the given sequence is of the form $$t_{ n }=\cfrac { n }{ n+1 }$$. Hence, the nth term of the sequence is $$t_{ n }=\cfrac { n }{ n+1 }$$.Maths

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