Question
If ^ -1 [ 1 1+1.2 ]+ ^ -1 [ 1 1+2.3 ]+ + ^ -1 [ 1 1+n(n+1) ]= ^ -1 [x], then x is equal to
BITSAT
Mathematics
Sequences and Series
2024
BITSAT 2024 (Memory Based Paper 2)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 1 n+1
- B. n n+1
- C. 1 n+2
- D. n n+2
Answer
D. n n+2
Step-by-step solution
aligned & Given ^ -1 ( 1 1+1.2 )+ ^ -1 ( 1 1+2.3 )+ \\ & + ^ -1 ( 1 1+n(n+1) )= ^ -1 (x) aligned aligned ^ -1 ( 2-1 1+1.2 ) & + ^ -1 ( 3-2 1+2.3 )+ \\ & + ^ -1 ( n+1-n 1+n(n+1) )= ^ -1 (x) aligned aligned & ^ -1 (2)- ^ -1 (1)+ ^ -1 (3)- ^ -1 (2)+ \\ & + ^ -1 ( n +1)- ^ -1 ( n )= ^ -1 (x) aligned ^ -1 ( n +1)- ^ -1 (1)= ^ -1 (x) \ ^ -1 (A)- ^ -1 (B)= ^ -1 ( A-B 1+A B ) \ ^ -1 ( n n+2 )= ^ -1 (x) x= n n+2
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