Question

Toate subpunctele din poza.

Answer 1

a)x=1+2+2²+2³+....+2²⁰¹=(2²⁰¹⁺¹-1)/(2-1)=2²⁰²-1
√x+1=√(2²⁰²-1+1)=√2²⁰²=2¹⁰¹


b)x=1+3+3²+3³+....+3²⁴⁹=(3²⁴⁹⁺¹-1)/(3-1)=(3²⁵⁰-1)/2
√2x+1=√[2(3²⁵⁰-1)/2+1]=√(3²⁵⁰-1+1)=√3²⁵⁰=3¹²⁵

c)x=1+5+5²+5³+....+5³⁵⁹=(5³⁵⁹⁺¹-1)/(5-1)=(5³⁶⁰-1)/4
√4x+1=√[4(5³⁶⁰-1)/4+1]=√(5³⁶⁰-1+1)=√5³⁶⁰=5¹⁸⁰

d)x=1+3²+3⁴+3⁶+....+3⁹⁸
x=1+3+3²+3³+3⁴+3⁵+3⁶+....+3⁹⁷+3⁹⁸+3⁹⁹-3-3³-3⁵-....-3⁹⁷-3⁹⁹
x=(3⁹⁹⁺¹-1)/(3-1) -3(1+3²+3⁴+3⁶+....+3⁹⁸)
x=(3¹⁰⁰-1)/2 -3x
4x=(3¹⁰⁰-1)/2
8x=3¹⁰⁰-1
√8x+1=√(3¹⁰⁰-1+1)=√3¹⁰⁰=3⁵⁰


e)x=1+6²+6⁴+6⁶+....+6¹⁹⁸
x=1+6+6²+6³+6⁴+6⁵+6⁶+....+6¹⁹⁷+6¹⁹⁸+6¹⁹⁹-6-6³-6⁵-....-6¹⁹⁷-5¹⁹⁹
x=(6¹⁹⁹⁺¹-1)/(6-1) -6(1+6²+6⁴+6⁶+....+6¹⁹⁸)
x=(6²⁰⁰-1)/5 -6x
7x=(6²⁰⁰-1)/5
35x=(6²⁰⁰-1)
√35x+1=√(6²⁰⁰-1+1)=√6²⁰⁰=6¹⁰⁰