Question

If f is a constant function of value 1/10.Then the value of f(1)+f(2)+f(3)+•••+f(100) is

Answer 1

Given:

f is a constant function of value 1/10

To Find:

• Value of f(1)+f(2)+....+f(100)

Constant Function:

A function which gives the same value for all values of provided variable(say x) is called constant function.

If f:R→R is a constant function

then f(x) is defined by f(x)=c, ∀ x∈R

where c is a constant

Solution:

Since, f is a constant function

So,

$\sf{f(1)=f(2)=f(3)=.........=f(100)=\dfrac{1}{10}}$

Now,

$\longrightarrow\sf{f(1)+f(2)+f(3)+.........+f(100)}$

$\longrightarrow\sf{\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}+.......\dfrac{1}{10}}$

On adding $\sf{\dfrac{1}{10}}$ 100 times, we get

$\longrightarrow\sf{100\bigg(\dfrac{1}{10}\bigg)}$

$\longrightarrow\sf{\pink{10}}$

Hence, the value of f(1)+f(2)+....+f(100) is 10.