The value of undersetx arrow 2lim displaystyle ∑ r = 17 (xr - 2r/2 r (x - 2)) is equal to

Question

The value of undersetx arrow 2lim displaystyle ∑ r = 17 (xr - 2r/2 r (x - 2)) is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

We have, displaystyle ∑ r = 17 undersetx arrow 2lim ((xr - 2r)/2 r (x - 2)) = displaystyle ∑ r = 17(r ⋅ 2r - 1/2 r)=(1 + 21 + 22 + . ldots .. + 26/2)=(127/2)

Q. The value of $x \to 2 l im r = 1 \sum 7 \frac{x ^{r} - 2 ^{r}}{2 r ( x - 2 )}$ is equal to

We have, $r = 1 \sum 7 x \to 2 l im \frac{( x ^{r} - 2 ^{r} )}{2 r ( x - 2 )}$
$= r = 1 \sum 7 \frac{r \cdot 2 ^{r - 1}}{2 r} = \frac{1 + 2 ^{1} + 2 ^{2} + . \dots .. + 2 ^{6}}{2} = \frac{127}{2}$

Q. The value of x→2lim​r=1∑7​2r(x−2)xr−2r​ is equal to

We have, r=1∑7​x→2lim​2r(x−2)(xr−2r)​ =r=1∑7​2rr⋅2r−1​=21+21+22+.…..+26​=2127​

Q. The value of $x \to 2 l im r = 1 \sum 7 \frac{x ^{r} - 2 ^{r}}{2 r ( x - 2 )}$ is equal to

We have, $r = 1 \sum 7 x \to 2 l im \frac{( x ^{r} - 2 ^{r} )}{2 r ( x - 2 )}$
$= r = 1 \sum 7 \frac{r \cdot 2 ^{r - 1}}{2 r} = \frac{1 + 2 ^{1} + 2 ^{2} + . \dots .. + 2 ^{6}}{2} = \frac{127}{2}$