Question

Aratati ca s= f(1)+f(2)+...+f(100) este patrat perfect
f(x)=2x-1

Answer 1

$f(x)=2x-1 \\\\ f(1)=2*1-1 =2-1 \to 1 \\ f(2)=2*2-1 =4-1 \to 3 \\.\\.\\.\\f(100)=2*100-1=200-1\to 199 \\\\ f(1)+f(2)+...+f(100)=1+3+....+199 \\\\\ =\frac{(1+199)}{\not2}*\not100= \\\\=200*50= \\\\ = 10000 \to 100^2 \ \ \ - \ este \ p.p.$

Answer 2

s=f(1)+f(2)+...+f(100)
f(x)=2x-1
f(1)=2-1
     =1
f(2)=4-1
     =3
f(100)=200=1=199
s=2+3+........+199
s=100*((199+1)/2)
s=100*(200/2)
s=100*100 =100²===>>>> ca suma f(1)+f(2)+.................f(100) este patrat perfect=100²