AP EAMCET · Maths · Sequences and Series
The value of the sum \(1 \times 2 \times 3+2 \times 3 \times 4+3 \times 4 \times 5+\ldots\) upto \(n\) terms is equal to
- A \(\frac{1}{6} n^2\left(2 n^2+1\right)\)
- B \(\frac{1}{6}\left(n^2-1\right)(2 n-1)(2 n+3)\)
- C \(\frac{1}{8}\left(n^2+1\right)\left(n^2+5\right)\)
- D \(\frac{1}{4} n(n+1)(n+2)(n+3)\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{4} n(n+1)(n+2)(n+3)\)
Step-by-step Solution
Detailed explanation
Let given series be \(S=1 \cdot 2 \cdot 3+2 \cdot 3 \cdot 4+3 \cdot 4 \cdot 5+\ldots n\) terms Now, general term…
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