Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The positive integer 'n' for which
2 × 2 2 + 3 × 2 3 + 4 × 2 4 + ……….n × 2 n = 2 n +10 is :
Text Solution
Verified by ExpertsThe correct answer is:
D
2 n+10 = 2×2 2 + 3×2 3 + 4 × 2 4 + …..n.2 n
2.(2 n+10 ) = 2×2 3 +3×2 4 +….(n–1).2 n +n.2 n+1
On subtracting we get :–
–2 n+10 = 2×2 2 + 2 3 + 2 4 +….2 5 +….2 n – n.2 n+1 – 2
n+10 = 8 + 
–n.2 n+1 ⇒ –2
n+10 = 8 + 8.2 n–2 – 8 – n.2 n+1 ⇒ – 2
n+10 = 2 n+1 – n. 2 n+1 ⇒ –2
n+10 = 2 n+1 (1– n)
⇒ –(2 n . 2 10 ) = 2 n . 2(1 – n)
⇒ 2 10 = 2n – 2
⇒ 1024 = 2n – 2
⇒ n = 513
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