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CGP EDU Academic Team
Published on: August 13, 2026
Prove that 1 2 .C 1 + 2 2 . C 2 + 3 2 . C 3 + ... n 2 . C n = n (n + 1) . 2 n– 2 where C r = n C r
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. L.H.S. = 
= 
n– 1 C r – 1
n 
= 
= n 
= n[(n–1))2 n–2 + 2 n–1 ]
= 2 n-2 . n [n – 1+ 2] = n (n + 1) . 2 n– 2
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