If Sn = 13 + 23 + ..... + n3 and Tn = 1 + 2 + 3 + ..... + n, then(a) S

1.	If Sn = 13 + 23 + ..... + n3 and Tn = 1 + 2 + 3 + ..... + n, then(a) Sn = \(T^2_n\)(b) Sn = \(T^3_n\)(c) \(S_n^2\) = Tn (d) \(S_3^2\) = Tn
Answer» (a) S_n = \(T_n^2\) Sn = ∑n³ = \(\frac{n^2(n+1)^2}{4}\) = \(\big(\frac{n(n+1)}{2}\big)^2\) ....(i) T_n = \(\frac{n(n+1)}{2}\) ......(ii) ∴ From (i) and (ii) S_n = \(T_n^2\)

If Sn = 13 + 23 + ..... + n3 and Tn = 1 + 2 + 3 + ..... + n, then(a) Sn = \(T^2_n\)(b) Sn = \(T^3_n\)(c) \(S_n^2\) = Tn (d) \(S_3^2\) = Tn

Answer»

(a) S_n = \(T_n^2\)

Sn = ∑n³

= \(\frac{n^2(n+1)^2}{4}\) = \(\big(\frac{n(n+1)}{2}\big)^2\) ....(i)

T_n = \(\frac{n(n+1)}{2}\) ......(ii)

∴ From (i) and (ii)

S_n = \(T_n^2\)