Prove that 1 2 . C 1 + 2 2 . C 2 + 3 2 . C 3 + ……..n 2 . C …

Maths Binomial Theorem & Mathematical Induction Mix Subjective Type

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

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The correct answer is:

CHECK THE SOLUTION.

Sol. Here, Δ QSF and Δ FI I ′ are similar triangles

Thus = ..... (1)

Again Δ TRF and Δ FO ′ O are similar triangles

Thus = ..... (2)

Since, QS = OO ′ and TR = I I ′

we get = or, =

Due to very small aperture and paraxial rays, S and T are very close to P so that

SP = TP = O.

∴ = ⇒

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