Question

Find the number of zeros in 100^1*99^2*98^3*97^4*96^5*______*1^100

Answer 1

1124 zeroes 100¹ * 99² * 98³ * 97⁴ * 96⁵ *..............................*2⁹⁹ * 1¹⁰⁰

Step-by-step explanation:

To get zeroes   we need  numbers ending with 0 & ending with 5

as 2 would be more than enough

100¹ = 2 zeros

90¹¹ = 11 Zeroes

80²¹ = 21 Zeroes

20⁸¹ = 81 Zeroes

10⁹¹ = 91 Zeroes

2 + 11 + 21 + ----------------------------81 + 91

= 1 + 1 + 11 + 21 + ----------------------------81 + 91

= 1 + (10/2)(1 + 91)

= 1 + 460

= 461

95⁶  = 6  Zeroes

85¹⁶  = 16 zeroes

75²⁶ = (5 * 5 * 3)²⁶ = 26 + 26 Zeroes

65³⁶ = 36 Zeroes

55⁴⁶ = 46 Zeroes

50⁵¹ = 51 Zeroes (only for 5)

45⁵⁶ =  56 Zeroes

35⁶⁶ = 66 Zeroes

25⁷⁶ = (5 * 5)⁷⁶ =  76 + 76 Zeroes

15⁸⁶ = 86 zeroes

5⁹⁶ = 96 zeroes

6 + 16 + 26 + 26 + 36 + 46 + 51 + 56 + 66 + 76 + 76 + 86 + 96

= 26 + 76 + 51 + (6 + 16 +................................+86 + 96)

= 153 + (10/2)(6 + 96)

= 153 + 510

= 663

461 + 663  =   1124

1124 zeroes

Learn more:

Find number of zeros in 1^1*2^2*3^3*....48^48*49^49?

https://brainly.in/question/11573195

Answer 2

Step-by-step explanation:

!100×!99×!98×!97×.........!2×!1

!5= 1 zero

!6= 1 zero

upto !9= 1zero

!5 to !9= 5 zero

!10 to !14= 2 each zero =10 zero

!15 to !19= 3each =15 zero

20 to 24 20 zero

that means

5+10+15+20+..........................90+95+24

5(1+2+3+4......19)+24

5×20×19/2+24

950+24

total 974