Sequences and Series

JEE Main 2025 (Online) 22nd January Morning ShiftMCQMedium📈 Topic in 24% papers+4−1

Ques. 1JEE Main 2025, 22 January (Morning Shift)

If r=1nTr= (2n-1)(2n+1)(2n+3)(2n+5)64, then n r=1n ( 1Tr ) is equal to :

Answer

(1) 23

Solution

Tn=Sn-Sn-1= (2n-1)(2n+1)(2n+3)8

1Tr=2 [ 1(2r-1)(2r+1)- 1(2r+1)(2r+3) ] (telescopes)

r=1n 1Tr=2 [ 13- 1(2n+1)(2n+3) ]

As n : 23

Answer: (1)

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Ques. 2JEE Main 2025, 22 January (Evening Shift)

Suppose that the number of terms in an A.P. is 2k, k . If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27, then k is equal to:

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