JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023limn→∞n3{4+(2+n1)2+(2+n2)2+⋯+(3−n1)2} is equal to
Choose the correct answer:
- A.
12
- B.
319
- C.
0
- D.
19
(Correct Answer)
19
Explanation
Solution
Is limit ko hum ek definite integral ki tarah likh sakte hain. Di gayi series ko summation form mein likhne par:
L=n→∞limn3r=0∑n−1(2+nr)2
Definite integral ke rule (nr→x,n1→dx,∑→∫) ka upyog karte hue:
L=3∫01(2+x)2dx
Ab iska integration karte hain:
L=3[3(2+x)3]01
L=(2+1)3−(2+0)3
L=33−23
L=27−8=19
Sahi Option: (4)
Explanation
Solution
Is limit ko hum ek definite integral ki tarah likh sakte hain. Di gayi series ko summation form mein likhne par:
L=n→∞limn3r=0∑n−1(2+nr)2
Definite integral ke rule (nr→x,n1→dx,∑→∫) ka upyog karte hue:
L=3∫01(2+x)2dx
Ab iska integration karte hain:
L=3[3(2+x)3]01
L=(2+1)3−(2+0)3
L=33−23
L=27−8=19
Sahi Option: (4)