Question

(Q). The value of x for which the equation
1+r+r²+...+r^x
= (1 + r) (1 + r) (1 + r4) (1 + r)
holds is :​

Answer 1

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=> (1 + r) (1 + r²) (1 + r⁴) (1 + r^8)

=> (1 + r + r² + r³)(1 + r⁴)(1 + r^8)

=> (1 + r + r² + r³ + r⁴ + r^5 + r^6 + r^7)(1 + r^8)

=> 1 + r + r² +....+ r^11 + r^12 + r^13 + r^14 + r^15

Thus, for x = 15, the equation

=> 1+r+r²+...+r^x

=> (1 + r) (1 + r²) (1 + r⁴) (1 + r^8)holds.

silentlover45.❤️

Answer 2

Answer:

=> (1 + r) (1 + r²) (1 + r⁴) (1 + r^8)

=> (1 + r + r² + r³)(1 + r⁴)(1 + r^8)

=> (1 + r + r² + r³ + r⁴ + r^5 + r^6 + r^7)(1 + r^8)

=> 1 + r + r² +....+ r^11 + r^12 + r^13 + r^14 + r^15

Thus, for x = 15, the equation

=> 1+r+r²+...+r^x

=> (1 + r) (1 + r²) (1 + r⁴) (1 + r^8)holds.