Que.5
The value of log 13+23+33+.........n3 is equal to:
H.
AO 3 log 1 + 3 log 2 +
+ 3 log n
B.O 2 log n + 2 log (n+1) - 2 log 2
co log n + log (n+1) + log (2n+1) - log 6
D.O 1
Answers
Answer:
option b is correct
Step-by-step explanation:
1^3+2^3+...+n^3=(n(n+1)/2)^2
hence
Given : log ( 1³ + 2³ + 3³ + _______ + n³)
To Find : Value :
A 3 log 1 + 3 log 2 + _____ + 3 log n
B 2 logn + 2log (n + 1) - 2log 2
C log n + log (n + 1) + log (2n + 1 - log 6
D 1
Solution:
log ( 1³ + 2³ + 3³ + _______ + n³)
∑n³ = (n (n + 1)/2) ²
log ( 1³ + 2³ + 3³ + _______ + n³)
= log (n (n + 1)/2) ²
log aⁿ = n log a
= 2 log (n (n + 1)/2)
log (ab/c) = loga + log b - log c
= 2 log n + 2 log (n + 1) - 2 log 2
Hence log ( 1³ + 2³ + 3³ + _______ + n³)
= 2 log n + 2 log (n + 1) - 2 log 2
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