Question

Identify a relationship among Tn , Sn and Sn-1 where n>1

Answer 1

$S_{n} - S_{n - 1} = T_{n}$

Step-by-step explanation:

Let the series have n terms and the sum of the n terms is given by $S_{n}$ and the sum of first (n - 1) terms is given by $S_{n - 1}$.

Let the series be $T_{1}, T_{2}, T_{3}, ................. , T_{n - 1}, T_{n}$.

Therefore, $S_{n} = T_{1} + T_{2} + T_{3} + .............. + T_{n - 1} + T_{n}$ ........... (1)

Again, $S_{n - 1} = T_{1} + T_{2} + T_{3} + .............. + T_{n - 2} + T_{n - 1}$ .............. (2)

Hence, $S_{n} - S_{n - 1} = T_{n}$ {From equations (1) and (2)} (Answer)