If 2 10 + 2 9 · 3 1 + 2 8 · 3 2 + … … + 2 · 3 9 + 3 10 = S - 2 11 , then S is…

If 210+29·31+28·32+……+2·39+310=S-211, then S is equal to
  1. 311-212
  2. 311
  3. 3112+210
  4. 2.311

Solution

S'=210+29·3+28·32+…….+2·39+310

S'=2101+32+322+…….+329+3210

G.P. →a=1,r=32,n=11

S'=210·3211-132-1=211311211-1

=311-211

Asked in: JEE Main 2020 (05 Sep Shift 1)

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