If 100=2(power a) .5(power b) then find a+B.
Answers
Answered by
1
Answer:
If 100=2(power a) .5(power b) then find a+B.
Step-by-step explanation:
Given that 100!=2
a
3
b
5
c
7
d
...
We know that a,b,c,d are the exponents of 2,3,5,7 in 100!,
∴ Coefficient of 2 in 100! is
a=[
2
100
]+[
2
2
100
]+[
2
3
100
]+[
2
4
100
]+[
2
5
100
]+[
2
6
100
]+...
where [] represents the integral part of the number respectively,
∴ a=50+25+12+6+3+1+0+...=97
The exponent of 3 in 100! is
b=[
3
100
]+[
3
2
100
]+[
3
3
100
]+[
3
4
100
]+...
=33+11+3+1+0+...
=48
The exponent of 5 in 100! is,
c=[
5
100
]+[
5
2
100
]+...
=20+4+0+...
=24
The exponent of 7 in 100! is,
d=[
7
100
]+[
7
2
100
]+...
=14+2+0+...
=16
,
∴ c=
2
b
and d=
3
b
hope it's helpful
Answered by
0
Answer:
300
Step-by-step explanation:
a=50,,
b=250
because 2 =100
1=50
5=250
Similar questions