JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023The sum 12−2⋅32+3⋅52−4⋅72+5⋅92−⋯+15⋅292 is ________.
Choose the correct answer:
- A.
6952
(Correct Answer) - B.
6953
- C.
6950
- D.
6951
6952
Explanation
Solution:
General term Tr ko do parts mein dekhte hain:
Agar r odd hai: r(2r−1)2
Agar r even hai: −r(2r−1)2
Poori series ka sum:
S=r=1∑15(−1)r−1r(2r−1)2
Ise expand aur simplify karne par (ya property use karne par):
S=1(1)2−2(3)2+3(5)2⋯+15(29)2
Calculation ke baad final sum:
Answer: 6952
Explanation
Solution:
General term Tr ko do parts mein dekhte hain:
Agar r odd hai: r(2r−1)2
Agar r even hai: −r(2r−1)2
Poori series ka sum:
S=r=1∑15(−1)r−1r(2r−1)2
Ise expand aur simplify karne par (ya property use karne par):
S=1(1)2−2(3)2+3(5)2⋯+15(29)2
Calculation ke baad final sum:
Answer: 6952