Correct Answer - Option 2 : 3
Calculation:
(1 + 0.0001)10000 which is similar to the form (1 + 1/n)n where n = 10000.
Using binomial expansion, we have
⇒ (1 + 0.0001)10000 = (1 + 1/n)n
⇒ 1 + n × 1/n + n(n-1)/2! × 1/n2 + [n(n-1)(n-2)]/3! × 1/n3 + ……..
⇒ 1 + 1 + 1/2!(1 – 1/n) + 1/3!(1 – 1/n) + (1 – 2/n) + ……
⇒ 1 + 1/1! + 1/2! + 1/3! + …..+1/(9999)!
⇒ 1 + 1/1! + 1/2! + 1/3! + …….∞
⇒ e < 3 as e = 2.73
∴ The positive integer just greater than (1 + 0.0001)10000 is 3.
⇒ (1 + x)n = nΣr=0 nCr . xr = [C0 + C1 x + C2 x2 + … Cn xn]
⇒ e = 1 + 1/1! + 1/2! + 1/3! + …….∞
