AP EAMCET · Maths · Binomial Theorem
What is the sum of the first \(n\)-terms of the series, whose \(k\)-term is \(k ! \times k\) ?
- A \((n+1) !^n-1\)
- B \((n+1)^n-1\)
- C \((n+1) !-1\)
- D \(3 n-2\)
Answer & Solution
Correct Answer
(C) \((n+1) !-1\)
Step-by-step Solution
Detailed explanation
Given, \(\begin{aligned} t_k & =k k !=(k+1-1) k ! \\ & =(k+1) k !-k !=(k+1) !-k !\end{aligned}\) \(\begin{aligned} & t_1=2 !-1 ! \\ & t_2=3 !-2 ! \\ & t_3=4 !-3 !\end{aligned}\) ......... ......... \(\underline{t_n=(n+1) !-n !}\) \(t_1+t_2+\ldots .+t_n=(n+1) !-1\) \(\therefore\)…
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