Question

.
6uF धारिता के तीन संधारित्र उपलब्ध हैं। उनके संयोजन से प्राप्त न्यूनतम एवं अधिकतम धारित
होगी​

Answer 1

Answer:

given series is 0.7 + 0.77 + 0.777 + ......... to nth term

therefore ,

S_nS

n

= 7×(0.1 + 0.11 + 0.111 +......to nth yerm)

=7/9 ( 0.9 + 0.99 + 0.999 + ...... to nth term )

=7/9 ( 9/10 + 99/100 + 999/1000 + ..... to nth term )

= 7/9 { ( 1 - 1/10 ) + ( 1 - 1/100 ) + ( 1 - 1/1000 ) + .... to nth term }

= 7/9 { 1+1+1+....to nth term } - { 1/10 + 1/100 + 1/1000 +.... to nth term}

= 7/9 { n - 1/10 ( 1 - 1/10 ) ^n / 1 - 1/10 }

= 7/9 { n - 1 ( 1 - 1/10 )^n / 9 }

= 7/9 { n - ( 1 - 1/10 )^n / 9 }

\huge\mathfrak\blue{ proved }proved.