### Eamcet - Maths - Mathematical Induction Test

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(13/1)+(13+23/1+3)+(13+23+33/1+3+5)+….. n terms

2.12+3.22+4.32+….+(n+1)n2=

1.2+2.3+3.4+….n terms

2.4+4.7+6.10+….(n-1) terms=

(1)+(1+2)+(1+2+3)+…. n brackets=

If nεN then 3.52n+1+23n+1 is divisible by

The sum of the first n terms of the series 12+2.22+32+2.42+52+2.62+…. Is n(n+1)2/2 when n is even. When n is odd the sum is

1+4+13+40+…n terms=

If 23+43+63+….+(2n)3=kn2(n+1)2, then k=

(1)+(2+3)+(4+5+6)+….n brackets=

The area bounded by y = 3x and y = x2 is (in sq units)

13+12+1+ 23+22+2+ 33+32+3+…3n terms=

2+3+5+6+8+9+…..2n terms=

1.4.7+4.7.10+7.10.13+…. n terms

13+23+ 33+….+1003=k2, then k=

1.3.4+2.4.5+3.5.6+…. n terms

1+4+10+19+….(3n2-3n+2)/2=

The equation of lines passing through the intersection of  lines x-2y+5=0 and 3x+2y+7=0 and perpendicular to x-y=0 is

∑((12+22+32+….+n2)/1+2+3+….+n)=

1.22+2.32+3/42+….n(n+1)2/12.2+22.3+32.4+…n2(n+1)=

Sum of n brackets of (1)+(1/3+1/32)+(1/33+1/34+1/35)+…. Is

12+32+52+…+(2n-1)2=

The value of the sum in the n th bracket of (1)+(2+3)+(4+5+6+7)+(8+9+10+15)+… is

(14/1.3)+(24/3.5)+(34/5.7)+….+n4/(2n+1)(2n-1)=

102n+1+1 for all n?N is divisible by

If nεN then 10n+3.4n+2+5 is divisible by

(12/3)+(12+22/5)+(12+22+32/7)+… n terms

(1)+(2+3+4)+(5+6+7+8+9)+… n brackets=

(1/1.3)+(1/3.5)+(1/5.7)+….n terms=

1.3+2.32+3.33+4.34+….+n.3n=

Note: