Problem Solving (PS) | Re: For a sequence t_1, t_2, t_3, ..., S_n denotes the sum of the first n

Solution

•\( S_n = n^3 + n^2 + n+1 = n^2(n + 1) + 1(n +1) = (n+1)(n^2 +1)\)
•\( t_m =291\)
•We need to find the value of m.
•Now,\( t_m = S_m – S_{m-1} = (m +1 )(m^2 + 1) – (m-1+1)((m-1)^2 +1)\)

o\( ⟹t_m = m^3 +m^2 +m+1 – m(m^2 -2m + 2)\)
o\( ⟹t_m = m^3 + m^2 +m+1 – m^3 +2m^2 –2m\)
o[m] ⟹ t_m
...

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