Question

The value of(1-1\5)(1-1\6)(1-1\7)...(1-1\100)

Answer 1

Though (1–1/2)(1–1/3)…(1–1/10^100) cannot possibly be calculated explicitly, you can conclude immediately that it is equal to 1/10^100 = 10^-100.my tata will answer this  use your brain if you have it

Answer 2

The product may be calculated by hand or by laptop by multiplying out the terms. however there's no reason to try and do this, since (1–1/n) = (n-1)/n, so the dividend of term i+1 is off by the divisor of term i. that the final answer is simply 1/5.

The beauty of this resolution is that

• It is precise
• It needs no long and erring calculation (n multiplications)
• It is true not withstanding what percentage terms you have got

Though (1–1/2)(1–1/3)…(1–1/10^100) cannot probably be calculated expressly, you'll conclude right away that it's adequate to 1/10^100 = 10^-100.

Mathematically,

• =(1 – 1/2) x (1 – 1/3) x (1 – 1/4) x (1 – 1/5)
• = (1/2) x (2/3) x (3/4) x (4/5)
• = (1 x 2 x 3 x 4)/(2 x 3 x 4 x 5)
• = 4! / 5!
• = 4! / (4! x 5) [ since n! = n x (n - 1) ]  
• = 1/5