Question

(-1)X(-1)x-(1)X.....(2m+1) times where m is a natural number is equal to

Answer 1

Answer:

(2m+1)where m is any natural number so,if is2 then (2m+1)=3if m=5then (2m+1)=11 so they are odd numbers always (-1)*(-1)*(1)*(2m+1) is(-1)^odd number=-1

Answer 2

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: .(2m+1) \: times } = -1$

Given :

The expression

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: .(2m+1) \: times }$

To find :

The value of the expression

Formula :

$\sf {( - 1)}^{n} = \begin{cases} & \sf{ \: \: \: 1\: \: \: \: when \: n \: is \: even} \\ \\ & \sf{ - 1\: \: \: \: \: when \: n \: is \: odd} \end{cases}$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: .(2m+1) \: times }$

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: .(2m+1) \: times }$

$\displaystyle \sf{ = {( - 1)}^{2m+1} }$

We know that

$\sf {( - 1)}^{n} = \begin{cases} & \sf{ \: \: \: 1\: \: \: \: when \: n \: is \: even} \\ \\ & \sf{ - 1\: \: \: \: \: when \: n \: is \: odd} \end{cases}$

Since m is a natural number

So 2m + 1 is a odd natural number

Hence we have,

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: .(2m+1) \: times }$

$\displaystyle \sf{ = {( - 1)}^{2m+1} }$

$\displaystyle \sf{ = - 1 }$

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