1
WB JEE 2008
Subjective
+2
-0

$$A = \left[ {\matrix{ 1 & 2 \cr 0 & 1 \cr } } \right]$$ then by the principle of mathematical induction, prove that $${A^n} = \left[ {\matrix{ 1 & {2n} \cr 0 & 1 \cr } } \right]$$

2
WB JEE 2009
Subjective
+2
-0

Show that, for a positive integer n, the coefficient of xk (0 $$\le$$ k $$\le$$ n) in the expansion of 1 + (1 + x) + (1 + x)2 + ....... + (1 + x)n is $${}^{n + 1}{C_{n - k}}$$.

3
WB JEE 2010
Subjective
+2
-0

Prove by induction that for all n $$\in$$ N, n2 + n is an even integer (n $$\ge$$ 1).

WB JEE Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12