Question

greatest integer function

Answer 1

if \(\large \lfloor{ \rfloor}\) is the Greatest integer function

find value of


\(\large \color{black}{\begin{align} \lfloor{\dfrac14+\dfrac{0}{50}\rfloor}+\lfloor{\dfrac14+\dfrac{1}{50}\rfloor}+\lfloor{\dfrac14+\dfrac{2}{50}\rfloor}+\cdots+\lfloor{\dfrac14+\dfrac{45}{50}\rfloor}=\hspace{1.5em}\\~\\

\end{align}}\)

Answer 2

first 37 terms would be zero
for GIF if 0<x<1 [x] =0
and till [1/4 + 37/50] all terms would be zero
and after that all terms will become 1
I confirmed the 37th term by using 1/4 + x/50 = 1
x will turn out to 37.5
so till 37th term it will be less than 1 so GIF= 0

Answer 3

is the answer 9 ?

Answer 4

Mathematica got 8.
Refer to the attachment.

Answer 5

ok thnks

Answer 6

?

Answer 7

is it the \(\lfloor\)floor function\(\rfloor\), or the \(\lceil\)ceiling function\(\rceil\)?