Sequences & Series
Series summation
nta_pyq_2025_apr
Grade 12
Question:
The sum$1 + 1+3$$1+3+5$$1+3+5+7$2! + 3! + 4! +$\ldots upto$$\infty terms, is equal to$
Step-by-Step Solution
Key Concept: Rewrite the finite series in a standard summation form and apply formulas for$\sum n$and$\sum n^2$.
$S = 1 + 1 + 3 + 1 + 3 + 5$+$\ldots 2$! 3!$(4)$$\infty 2 r =$$\sum r$!$r=1$$\infty$$\infty$$\infty ($r - 1 + 1)$1 1 =$$\sum =$$\sum +$$\sum ($r - 1$)$! ($r - 2)$! ($r - 1)$!$r=1$$r=2$$r=1 = 2e$
Correct Answer: 4