Question : What is the value of (22 + 1)(24+1)(28 + 1)(216 + 1) .........(2128 + 1)?
Option 1: $\frac{2^{256}-1}{2}$
Option 2: $\frac{2^{256}-1}{3}$
Option 3: $2^{256}-1$
Option 4: $\frac{2^{256}-1}{4}$
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: $\frac{2^{256}-1}{3}$
Solution :
$(2^2 + 1) (2^4 + 1) (2^8 + 1) (2^{16} + 1) ........ (2^{128} + 1)$
Divide by $(2^2 - 1)$ in numerator and denominator
= $\frac{1}{(2^2 - 1)}[(2^2 - 1)(2^2 + 1) (2^4 + 1) (2^8 + 1) (2^{16} + 1) ........ (2^{128} + 1)]$
= $\frac{1}{(2^2 - 1)}[(2^4 - 1) (2^4 + 1) (2^8 + 1) (2^{16} + 1) ........ (2^{128} + 1)]$
= $\frac{1}{(2^2 - 1)}[(2^8 - 1) (2^8 + 1) (2^{16} + 1) ........ (2^{128} + 1)]$
= $\frac{1}{(2^2 - 1)}[(2^{16} - 1) (2^{16} + 1) ........ (2^{128} + 1)]$
= $\frac{1}{(2^2 - 1)}(2^{256} - 1)$
= $\frac{(2^{256} - 1)}{3}$
Hence, the correct answer is $\frac{(2^{256} - 1)}{3}$.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
