Question

Find the sum upto nth term in the given series

4 + 44 + 444 + - - - - to nth term

spam = 10 answers report​

Answer 1

..Question..

Find the sum upto nth term in the given series

4 + 44 + 444 + - - - - - - to nth term

..Answer..

The given term is ➪

= 4 + 44 + 444 + - - - - - - - to nth term

= ( 4 + 44 + 444 + - - - - - - - to nth term )

= 4 ( 1 + 11 + 111 + - - - - - - to nth term )

= 4/9 ( 9 + 99 + 999 + - - - - - - to nth term )

= 4/9 { (10-1) + (100-1) + (1000-1) + - - - to nth term }

= 4/9 { ( 10 + 100 + 1000 + - - - to nth term ) - ( 1 + 1 + 1 + - - - to nth term ) }

= 4/9 [ { 10 × { ( 10 )^n - 1 } / ( 10 - 1 ) - n ]

= 4/9 { 10 ( 10^n - 1 ) / 9 - n }

____________________

Give a look here ,

• To calculate AP
• ➪ a + ( n - 1 ) d
• To calculate AP
• ➪ b - a = c - b

ㅤㅤㅤ꧁ ʙʀᴀɪɴʟʏ×ᴋɪᴋɪ ꧂

ㅤ

Answer 2

Now,

.4+.44+.444+_____ to n terms

=

9

4

(.9+.99+.999+_____ to n terms)

=

9

4

{(1−.1)+(1−.01)+(1−.001)+_____ to n terms

Step-by-step explanation:

The prince sent the sapphires for the playwright so that he could finish a play for the director of the theatre in time. The princes sent his second sapphire to a poor match girl. Her matches had fallen into the gutter. She was afraid that her father would beat her for this loss.