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Show that :-(1+5^-1)(1+5^-2)(1+5^-3)... (1+5^-2^n) = (5/4)(1-5^-2^n+1)?

Show that :-(1+5^-1)(1+5^-2)(1+5^-3)... (1+5^-2^n) = (5/4)(1-5^-2^n+1)?

Grade:11

1 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
7 years ago
Hi,

Just multiply and divide by (1-1/5).
SO you will see that the first term and the term we introduced are forming the (a-b)(a+b) form. Write this as a^2-b^. Now see the next term , we are again getting (a-b)(a+b) form So in this way each and every next term will be of same form and see the last term. You will get the answer in the same fashion.

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