What is the value of (1-(1/2)²) (1-(1/3)²) (1-(1/4)²) (1-(1/5)²)...... (1-(1/1024)²) ?

• a2-b2 = (a-b) (a+b)
  The equation given after simplification becomes (1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4).... = 1/2 * 3/2 * 2/3 * 4/3 * 3/4 .... 1025/1024..
  All terms except 1/2 and 1025/1024 will get cancelled.
  The answer is
  1/2 * 1025/1024 = 1025/2048.
  Hope this helps.
• 9 years agoHelpfull: Yes(59) No(1)
• ans=1025/2048
  (a-b)^2=(a-b)(a+b)
  after solving this series we get only first -ve part of first term and last +ve part of last term and remaining will be cancel
  i.e 1/2*1025/1024=1025/2048
  i.e
• 9 years agoHelpfull: Yes(1) No(4)
• use (a^2-b^2)=(a+b)*(a-b)
  ans is 1025/2048
• 9 years agoHelpfull: Yes(0) No(1)
• A staircase contains 12 steps. We can climb it 1 or 2 steps. But 8th step contains a snake so we cant step on it. In how many ways can we the top? Please solve this question
  
• 9 years agoHelpfull: Yes(0) No(3)
• oh sorry---a^2-b^2=(a-b)(a+b)
• 9 years agoHelpfull: Yes(0) No(2)