Choose the Correct options
0 of 25 Questions completed
Questions:
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
0 of 25 Questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Average score 

Your score 

\(a^n b^n \) is divisible by ____________., (where \( a \) & \( b \) are distinct.)
For is true.
For
, is divisible by .
is true.
, is divisible by .
For all \( n \geq 2, n^2 (n^41) \) is divisible by ___________.
For is true.
For is true by induction hypothesis.
is divisible .
For each \( n \in N \), the correct statement is ___________.
is true.
, is true.
is true.
is true by induction hypothesis.
is true.
For each \( n \in N , 10^{n2} > 81n\) if __________.
is false.
is false.
is false.
is false.
is true.
is true.
For is true, .
For is true by induction hypothesis.
is true if .
If \(a_n=2^{2^n}+1 \), for \(n > 1, (n=2a) a \in N \), the last digit of \( a_n \) is___________.
For
For
For
The last digit of , if is even.
\(1+3+3^2+…+3^{n1} \) is ___________.
For is true.
For
is true.
is true.
\(1+\dfrac{1}{(1+2)}+\dfrac{1}{(1+2+3)}+…+\dfrac{1}{(1+2+…+n)} \) is equal to ____________.
For is true.
For
is true by induction hypothesis.
.
\(f(n)=1\cdot3+2\cdot3^2+…+n \cdot3^n \) is equal to _____________.
For is true.
is true by induction hypothesis.
is true, .
\( f(n)=1\cdot 2+2\cdot 2^2+3\cdot 2^2+…+n\cdot2^n \) is equal to __________.
For is true.
is true by induction hypothesis.
.
\(f(n)=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+…+\dfrac{1}{2^n} \) is equal to _______________.
For is true.
For
, is true.
is true.
is true.
\( f(n)= \dfrac{1}{2\cdot 5}+ \dfrac{1}{5\cdot 8}+ \dfrac{1}{8\cdot 11}+…+ \dfrac{1}{(3n1)(3n+2)} \) is __________.
For is true.
is true by induction hypothesis.
.
\(f(n)= a+an+an^2+…+an^{n1} \) is equal to ___________.
For is true.
is true by induction hypothesis.
.
\( f(n)= \left ( 1+\dfrac{3}{1} \right )\left ( 1+\dfrac{5}{4} \right )\left ( 1+\dfrac{7}{9} \right )…\left ( 1+\dfrac{(2n+1)}{n^2} \right ) \) is equal to________.
For is true.
is true by induction hypothesis.
.
\( f(n)= \left ( 1+\dfrac{1}{1} \right )\left ( 1+\dfrac{1}{2} \right )\left ( 1+\dfrac{1}{3} \right )…\left ( 1+\dfrac{1}{n} \right ) \) is equal to________.
For is true.
, is true.
.
\( f(n)=1^2+3^2+5^2+…+(2n1)^2 \) is equal to ___________.
For is true.
is true by induction hypothesis.
.
\( f(n)=\dfrac{1}{1\cdot4}+\dfrac{1}{4\cdot7}+\dfrac{1}{7\cdot10}+…+\dfrac{1}{(3n2)(3n+1)} \) is _________.
For is true.
is true by induction hypothesis.
.
\( f(n)=x^{2n}y^{2n}\) is divisible by___________.
For is true.
For
, is divisible by
is true.
is true, .
\(f(n):1+2+3+…+n <\dfrac{1}{8}(2n+1)^2 \), if________.
, is true.
, it is true.
For is true.
For is true by induction hypothesis.
, is true for all .
\(f(n): (2n+7) < (n+3)^2 \) is true if _______.
, it is true.
, it is true.
For is true.
By induction hypothesis we will get that for is true.
is true, .
\( 3^{2n+2}8n9 \) is divisible by _________.
For , is true.
for is true by induction hypothesis.
is divisible by .
\(1^2+2^2+…+n^2 >\dfrac{n^3}{3} \) is true if ___________.
, is true.
, is true.
, is true.
For , is true.
By induction hypothesis is true.
.
\(f(n):2^n > n \) is true if _________.
, is true.
, is true.
For , is true.
For is true by induction hypothesis.
\(f(n): (1+x)^n \geq (1+nx) \), where \( n > 1 \) is true if______________.
, is true.
is true.
For is true.
For is true by induction hypothesis.
\(f(n)=11^n2^n \) is divisble by_______.
For is true.
For ,
, true.
is divisible by .
\(P(n):\dfrac{4^n}{n+1} < \dfrac{(2n)!}{(n!)^2} \), then \(P(n) \) is true for_______.
, is not true.
, is true.
is true for .