AP EAMCET · Maths · Sequences and Series
If \(\mathrm{S}_{\mathrm{n}}=1^3+2^3+\ldots. .+\mathrm{n}^3\) and \(\mathrm{T}_{\mathrm{n}}=1+2+\ldots. .+\mathrm{n}\), then
- A \(\mathrm{S}_{\mathrm{n}}=\mathrm{T}_{\mathrm{n}^3}\)
- B \(\mathrm{S}_{\mathrm{n}}=\mathrm{T}_{\mathrm{n}}^3\)
- C \(\mathrm{S}_{\mathrm{n}}=\mathrm{T}_{\mathrm{n}^2}\)
- D \(S_n=T_n^2\)
Answer & Solution
Correct Answer
(D) \(S_n=T_n^2\)
Step-by-step Solution
Detailed explanation
\( \mathrm{S}_{\mathrm{n}} = \left( \frac{\mathrm{n}(\mathrm{n}+1)}{2} \right)^2 \) \( \mathrm{T}_{\mathrm{n}} = \frac{\mathrm{n}(\mathrm{n}+1)}{2} \) \( \mathrm{S}_{\mathrm{n}} = \mathrm{T}_{\mathrm{n}}^2 \)
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