Question

Tính:

a)A=4+2²+2³+2⁴+..............+2²⁰

b)Tìm x biết:(x+1)+(x+2)+........+(x+100)=5750

Answer 1

a,2A=8+2³+2⁴+2⁵+............+2²¹

2A-A=(8+2³+2⁴+2⁵+...........+2²¹)-(4+2²+2³+2⁴+.............+2²⁰)

A=(8+2³+2²¹)-(4+2²)

A=8+8+2²¹-4-4

A=4+4+2²¹

A=2³+2²¹

b,(x+1)+(x+2)+.............+(x+100)=5750

=>x+1+x+2+...........+x+100=5750

=>100x+(1+2+............+100)=5750

=>100x+\(\frac{100.\left(100+1\right)}{2}\)=5750

=>100x+5050=5750

=>100x=5750-5050

=>100x=700

=>x=700:100

=>x=7