Answer :

Ekman
4+44+444+....... upto n terms.
4(1+11+111+........upto n terms)
4/9(9+99+999+.........upto n terms)
4/9[(10-1)+(10²-1)+...... upto n terms]
4/9[10+10²+.........+10ⁿ}-(1+1+1+....n times)]
(4/9) { 10 [ ( 10ⁿ - 1 ) / ( 10 - 1 ) ] - n(1) }
(4/9) [ (10/9) ( 10ⁿ - 1 ) - n ]...................
rekhaverma02021975

Answer:

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

= 4 [ 1 + 11 + 111 + ... to n terms ]

= (4/9) [ 9 + 99 + 999 + ... to n terms ]

= (4/9) [ (10 - 1) + (10² - 1) + (10³ - 1) + ... + (10ⁿ - 1) ]

= (4/9) [ ( 10 + 10² + 10³ + ... + 10ⁿ ) - ( 1 + 1 + 1 + ... n times ) ]

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

= (4/9) [ (10/9) ( 10ⁿ - 1 ) - n ] ................................. Ans-

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