Suppose r = 0 2023 r 2 C r 2023 = 2023 × × 2 2022 . Then the value of is ___________ . [2023]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
Suppose $\sum_{r = 0}^{2023} r^{2} {}^{2023}{C_{r}} = 2023 \times α \times 2^{2022}$ . Then the value of $α$ is ___________ . [2023]

Ans.
(1012)

$\sum_{r = 0}^{2023} r^{2}$ ${}^{2023}{C_{r}} = 2023 \times α \times 2^{2022}$

$\sum_{r = 0}^{n} r^{2} \cdot {}^{n}{C_{r}} = n (n + 1) \cdot 2^{n - 2}$

Then, $\sum_{r = 0}^{2023} r^{2} \cdot {}^{2023}{C_{r}} = (2023) (2023 + 1) \cdot 2^{2023 - 2}$

$= 2023 \times 2024 \times 2^{2021} = 2023 \times α \times 2^{2022}$

$∴$ $2 α = 2024 \Rightarrow α = 1012$

Want Us to Email you About Special Offers & Updates?