Question

Find an expression for the nth term (t_n) in each of the following​

Answer 1

`\boxed{\pink{\tt\longmapsto The \ nth \ term \ of \ the \ sequence\ is \ given \ by (1)/(n)}}`

Explanation:

A sequence is given to us is , and we need to find expression for nth term of the sequence. The given sequence is ,

`\boxed{\boxed{\blue{\qquad\bf 1 , (1)/(2),(1)/(3),(1)/(4),(1)/(5),(1)/(6)}}}`

When we flip the numbers , we can clearly see that the number are in Harmonic Progression.

That is when we flip the numbers they are found to be in Arithmetic Progression .

And nth term of an Harmonic Progression is :-

`\boxed{\purple{\bf T_((Harmonic \ Progression)) = (1)/(a+(n-1)d)}}`

Hence here

• Common difference = 1
• First term = 1 .

Substituting the respective values,

`\bf\implies T_(n)= (1)/(a+(n-1)d) \\\\\bf\implies T_(n) = (1)/(1+(n-1)1)\\\\\bf\implies T_n = (1)/(1+n-1)\\\\\bf\implies\boxed{\red{\bf T_(n)=(1)/(n)}}`

Hence the nth term of the given sequence is given by ¹/n .