Question
Download Solution PDFIf an = n(n!), then what is a1 + a2 + a3 +...+ a10 equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
n! = n × (n - 1) × (n - 2) × ....... × 3 × 2 × 1
Calculation:
an = n (n)!
an = (n + 1 - n)n!
an = (n + 1)n! - n!
an = (n + 1)! - n!
Hence,
a1 = 2! - 1!
a2 = 3! - 2!
----------------
a10 = 11! - 10!
Now,
a1 + a2 + a3 +...+ a10
2! - 1! + 3! - 2! + ......11! - 10!
= 11! - 1
∴ The value of a1 + a2 + a3 +...+ a10 is 11! - 1.
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